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# Finding Factors of 625: A Comprehensive Guide

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To find the factors of 625, we need to identify all the possible pairs of numbers that multiply to give 625. Here's how to do it step-by-step:

Step 1: List the first few positive integers.

We start by listing the first few positive integers: 1, 2, 3, 4, 5, ...

Step 2: Locate the number pairs which when multiplied, result in 625. To accomplish this task, we must determine all possible combinations of numbers from the given list that can produce a product of 625. Initially, dividing 625 by each digit on the list and verifying whether it yields an integer value may be useful.

For example, we can divide 625 by 1 and see that the result is 625. That means that 1 multiplied by 625 equals 625 so (1,625) is a pair of factors for 625. We then try dividing it by 2,3 and 4 to find more pairs of factors. If a number gives us a decimal or fractional remainder when divided into 625 then it isn't a factor.

625 ÷ 1 = 625

625 ÷ 2 = 312.5 (not a whole number)

625 ÷ 3 = 208.33 (not a whole number)

625 ÷ 4 = 156.25 (not a whole number)

625 ÷ 5 = 125

625 ÷ 6 = 104.17 (not a whole number)

625 ÷ 7 = 89.29 (not a whole number)

625 ÷ 8 = 78.125 (not a whole number)

625 ÷ 9 = 69.44 (not a whole number)

625 ÷ 10 = 62.5 (not a whole number)

We can see that the only pair of numbers that multiply to give 625 is 5 × 125.

Step 3: Write down all the factors.

The factors of 625 are the pairs of numbers that we found in step 2, plus 1 and 625 itself. Therefore, the factors of 625 are:

1, 5, 25, 125, 625

In conclusion, the factors of 625 are all the pairs of numbers that multiply to give 625, plus 1 and 625 itself. By following the steps outlined above, we can easily find the factors of any number.

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