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# What goes into 231?

To determine factors of a number it is necessary to divide the number by prime numbers of increasing value. If there is no remainder then the Prime number is a factor. The square root of 231 is approximately 15 so it is necessary to divide by all the prime numbers up to 13 (15 is not a prime number).

231 ÷ 2 leaves a remainder of 1

231 ÷ 3 divides exactly 77 times (which is 7 x 11 - both are prime numbers)

231 ÷ 5 leaves a remainder of 1

231 ÷ 7 divides exactly 33 times (which is 3 x 11 - both are prime numbers)

231 ÷ 11 divides exactly 21 times (which is 3 x 7 - both are prime numbers)

231 ÷ 13 leaves a remainder of 10

If we multiply together the three numbers that are shown to be factors 3 x 7 x 11 = 231

this confirms that there are no other factors of 231 except 1 and 231 itself. This last condition is true for every positive integer.

231 is divisible by 1, 3, 7, 11 and 231

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Q: What goes into 231?