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There are a few ways to go about factoring. You can decide what works best for you. I always find the prime factorization first. Let's look at a random number: 108

The prime factorization can be found by using a factor tree.

108

54,2

27,2,2

9,3,2,2

3,3,3,2,2

2^2 x 3^3 = 108

Half of the factors will be less than the square root, half greater. If the number is a perfect square, there will be an equal number of factors on either side of the square root. In this case, the square root is between 10 and 11.

Adding one to the exponents of the prime factorization and multiplying them will tell you how many factors there are. In this case, the exponents are 2 and 3. Add one to each. 3 x 4 = 12

108 has 12 factors. Six of them are 10 or less, six of them are 11 or greater. All we have to do is divide the numbers one through ten into 108. If the result (quotient) turns out to be an integer, you've found a factor pair. Knowing the rules of divisibility will make that even easier.

108 is divisible by...

1 because everything is.

2 because it's even.

3 because its digits add up to a multiple of 3.

4 because its last two digits are a multiple of 4.

6 because it's a multiple of 2 and 3.

9 because its digits add up to a multiple of 9.

That's six factors less than 10. Divide them into 108. That's the rest of them.

(108,1)(54,2)(36,3)(27,4)(18,6)(12,9)

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

Notice that all of those numbers, except for 1, can also be found in the prime factorization.

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Q: What is a way to break down a number into its factors?
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To find the factors of a number, I suggest using a factor tree. It is elementary, but it is undeniably the simplest way. Start with the number, in this case 62.62Pick any two factors and write them under the original number.622 x 31Circle (or bold) the prime numbers. These can no longer be divided. (In this case, both factors of 62 are prime. Otherwise, you would further break down the actors until you are only left with primes)In conclusion, the factors of 62 are 1, 2, 31, and 62. 2 and 31 are the prime factors of 62.


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A factor is a divisor - a number that will evenly divide into another number. One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them. The factors of 21 are 1, 3, 7, and 21. The factors of 27 are 1, 3, 9, and 27. The common factors are 1 and 3. This means that the greatest common factor is 3.


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List all the factors of 62?

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