What are all the factors of 300 and how do you know these are factors?

Answer 1

Start with the prime factorization.

2^2 x 3^1 x 5^2 = 300

Add one to the exponents and multiply.

3 x 2 x 3 = 18

300 has 18 factors.

Nine of them will be less than the square root, nine will be greater.

The square root of 300 is between 17 and 18.

If we test all the numbers 1 to 17, we will find nine factors. Knowing the rules of divisibility will show us which ones to test.

1 is because 1 always is.

2 is because it's even.

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

4 is because it's a multiple of 100.

5 is because it ends in zero.

6 is because 2 and 3 are.

10 is because it ends in zero

That leaves us two more between 10 and 17. Looking at the numbers we already have, I'd be tempted to test 12 and 15. Dividing those numbers into 300 gives us the rest.

All Factors of 300:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

Answer 2

Answering this question fully would be time-consuming and counterproductive. It is the intent of this forum to give you information, perhaps a few examples, so that you can solve such problems yourself.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

2 and 5 are prime.

101 is a Prime number. Its only factors are 1 and 101.

Your turn.

Answer 3

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300. They are the only numbers that will divide evenly into 300 with no remainder.

Answer 4

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300