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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.

Q: How do you work out the factors of a number?

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Continue Learning about Basic Math

I assume you are asking how do you work out the factors of a prime number. A prime number by definition only has itself and 1 as factors.

It has more than two factors.

Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.

There is NO number with the most number of factors.

A number that has more than two factors is a composite number whereas a number that has only two factors is a prime number.

Related questions

I assume you are asking how do you work out the factors of a prime number. A prime number by definition only has itself and 1 as factors.

if you mean what is an odd number whose has the same number of factors as the number itself... then 1 will work.

1,2,3,4,6,12

It has more than two factors.

Work out if they have any factors, other than the number 1 and themselves. If they do not they are prime.

Multiplication

The factors of 28 are 1,2,4,7,14 and 28. "Common" means "same for both". For these factors to be common, they need to be compared to the factors of another number.

Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.

I would pick any prime number and calculate it to the 14th power.

you can find the factors of a number my using a factor tree

Multiply the factors. They should equal the original number.

If a number has more than two factors, it's composite.