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Pair factors of 4500 are the pairs of numbers that when multiplied give the product 4500. The factors of 4500 in pairs are:

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Keep in mind that while deploying automatic lubrication systems can free personnel from time-consuming basic activities to provide extra value, it cannot replace staff who can deliver value at this level.

Relubrication quantities are dictated by the physical space available in the bearing, while relubrication intervals are dictated by the working conditions that determine the degradation rate of the lubricant (speed, load, temperature, type of bearing, etc.).

The factors of 4500 are too many, therefore if we can find the prime factorization of 4500, then the total number of factors can be calculated using the formula shown below. If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1). Prime Factorization of 4500 = 22 × 32 × 53 Therefore, the total number of factors are (2 + 1) × (2 + 1) × (3 + 1) = 3 × 3 × 4 = 36

Lubrication is an essential part of machinery maintenance for nearly every production facility. On average, lubricant purchases amount to only 3 percent of a maintenance budget, but lubrication-related activities can influence an estimated 40 percent of total maintenance costs.

Factors of 4500 are pairs of those numbers whose products result in 4500. These factors are either prime numbers or composite numbers.

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Consequently, parameters like pumpability and oil separation must be taken into account when an automatic lubrication system is to be installed. Furthermore, relubrication intervals must be defined in a way that prevents the lubricant from being stationary inside the lubrication ducts, especially when exposed to extreme temperatures that could promote premature degradation. Failure to understand and act on these issues can affect the performance and associated benefits of deploying an automatic lubrication system.

This example shows the benefit of accurately delivering the right quantity of lubricant (the second “R”), but what about the frequency of lubrication (the third “R”)?

The maturity level of a maintenance program (corrective, preventive, predictive, etc.) will dictate the skill and knowledge level required of personnel involved in lubrication-related activities.

Extending relubrication intervals beyond the calculated limits will expose the lubricant to excessive degradation and the bearing to lubricant starvation conditions. On the contrary, shortened relubrication intervals with adjusted quantities would renew the lubricant’s properties.

In order to achieve optimum reliability and maximum benefits from a lubrication program, several factors need to be taken into account. These factors are summarized by the well-known five “R”s of lubrication:

Simply using automation doesn’t guarantee success. The technology must be considered an instrument to achieve a goal. Basic decisions and activities must still be performed. The following are typical mistakes that can jeopardize the potential benefits of deploying automatic lubrication.

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As the maturity of maintenance and associated lubrication programs increases, so does the complexity of tasks that lubrication technicians must be capable of completing. These include activities such as:

Automatic lubrication alone certainly is not the solution to all your lubrication issues. It must be properly understood to boost its potential benefits. However, there are solutions available in the market for virtually every application, so it is difficult to imagine that a critical application is not worth equipping with an automatic lubrication device.

A single-point automatic lubrication system can deliver the right amount of grease at the right time to each lubrication point. This reduces both grease waste and the risk of bearing failure.

Further dividing 1125 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1125 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

The factors of 4500 and 2242 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and 1, 2, 19, 38, 59, 118, 1121, 2242 respectively. Common factors of 4500 and 2242 are [1, 2]. Hence, the Greatest Common Factor (GCF) of 4500 and 2242 is 2.

By comparison, a properly installed single-point automatic lubricator can supply a continuous and accurate flow of fresh and clean lubricant, keeping the application in proper condition while at the same time preventing contaminant ingress.

The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -125, -150, -180, -225, -250, -300, -375, -450, -500, -750, -900, -1125, -1500, -2250, -4500.

Having an automatic lubrication device doesn’t mean that the system won’t require any inspection. Regular inspection will help ensure the best results from an automated system. Inspection also will help to identify installation issues (damaged fittings, leaking or blocked pipes, lubricators not dispensing at the right pace, etc.) and spot when it’s time to change or refill lubricants.

In the previous example, the technician will relubricate the given point 52 times a year. As a result, the bearing will be exposed 52 times to external contamination as well as to over- and under-lubrication.

Moreover, lubrication routes must be updated, and manual lubrication tasks must be replaced with inspection tasks at an adequate interval. The frequency of inspection is less than that required for manual relubrication, but it still must be planned.

Processes must be clean to ensure no external contamination ingress to the grease, and each lubrication point should have a cap on its grease fitting. In addition, the utmost clean relubrication process for each point must be followed every time.

Therefore, as more mature maintenance programs are adopted, the areas where skilled maintenance technicians can add value to your operations need to be carefully considered. For example, are they best utilized performing manual relubrication, which can easily be automated, or by using their skills and knowledge to perform more analytical tasks, lubricant analysis and making improvements to the lubrication program?

The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and factors of 1756 are 1, 2, 4, 439, 878, 1756. Therefore, the Least Common Multiple (LCM) of 4500 and 1756 is 1975500 and Greatest Common Factor (GCF) of 4500 and 1756 is 4.

Factors of 4500 are integers that can be divided evenly into 4500. There are total 36 factors of 4500, of which 2, 3, 5 are its prime factors. The Prime Factorization of 4500 is 22 × 32 × 53.

The pair factors of 4500 are (1, 4500), (2, 2250), (3, 1500), (4, 1125), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), (60, 75).

Lubricant contamination will also affect bearing life and increase the risk of failure. In manual lubrication programs, avoiding grease contamination can be a challenge.

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When we divide 4500 by 3571 it leaves a remainder. Therefore, the number 3571 is not a factor of 4500. All numbers except 3571 are factors of 4500.

Of course, deploying an automatic lubrication system requires some level of investment. To maximize the return on that investment, the key is to choose the right solution based on the requirements and criticality of the application. Typical solutions range from inexpensive single-point automatic lubricators to very complex centralized systems with various options for online monitoring. Determining which option is best for your application depends to a great extent on your criticality analysis.

The simple task of pushing a lever on a grease gun to provide manual lubrication can be easily replaced by a machine. However, the real issue is whether you are getting the maximum value from your skilled maintenance technicians. Such personnel can manage a lubrication program through:

Besides lubricant costs, half of acquired components require relubrication. Overtime labor is mostly a result of machine failures typically caused by inadequate lubrication. In addition, approximately 5 percent of labor costs can be attributed to lubrication activities.

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There are many advantages in using automatic lubrication systems. These include reduced waste and risk of bearing failure, cleanliness, less labor, and improved environmental health and safety.

The fourth “R” refers to best practices, such as tagging and color-coding (or other methodology) of both lubrication points and tools in order to avoid cross-contamination.

Improper relubrication activities can have a significant impact on the environment. Consider again the grease waste calculations in the previous example. Now try to estimate the impact of this waste on the environment. Naturally, it depends on the disposal practices you implement at your facilities, but in basic environmental terms, the less waste the better.

If we assume the technician is satisfied with two strokes (if he doesn’t see any grease coming out of the seals), then after a year the bearing will receive 156 grams (52 weeks times 3 grams per week) instead of 104 grams (52 weeks times 2 grams per week). This means that up to 52 grams (50 percent) of grease will be wasted.

The fifth “R” can be defined once the application conditions, asset criticality and maintenance strategy are analyzed. This will help you make the decision on whether to automate each lubrication point. In order to make that decision, the pros and cons of automatic lubrication should also be understood and considered.

Since, the factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and the factors of 4128 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 43, 48, 86, 96, 129, 172, 258, 344, 516, 688, 1032, 1376, 2064, 4128. Hence, [1, 2, 3, 4, 6, 12] are the common factors of 4500 and 4128.

Next, consider points that are difficult or even hazardous to access and the potential impact to your personnel. This is another area where automatic lubrication systems offer real benefits.

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As a fundamental in any lubrication program, the lubricant selection must precede the lubrication system selection. After all, the lubricant that goes into the application is what lubricates, not the delivery system itself.

The lubricant and the automatic lubrication device must complement each other to ensure a better overall performance. Needless to say, not all lubricants are suitable for all automatic lubrication systems, and the impact of a lubrication system on the structure of the lubricant depends on the technology of that given lubrication system.

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To find the factors of 4500, we will have to find the list of numbers that would divide 4500 without leaving any remainder.

The starting point of an effective lubrication program is the detailed mapping of all lubrication points, including their working conditions, lubrication requirements and criticality. This information is needed to select the most suitable lubricant and the quantity of lubricant needed, as well as to calculate the adequate relubrication intervals. These are the first three “R”s.

For example, consider a bearing that needs to be relubricated with 2 grams of grease every week. With a standard grease gun, this would mean that the bearing should receive about 1.3 “strokes.” However, manually delivering 0.3 strokes is difficult. In reality, two strokes would likely be given. In other words, the bearing would receive 3 grams instead of 2 grams of lubricant each time.

To illustrate this point, consider that on average, a human being requires about 2,000 calories per day. Would you rather consume your weekly total of 14,000 calories once a week or in nearly equal amounts over seven days?