How to Find the Smallest Number That a Number Is Divisible By
All numbers are divisible by themselves and 1. Some numbers -- called prime numbers -- are only divisible by themselves and 1. Other numbers -- called composite numbers -- have other factors. You can use several simple tricks to find out whether a number is prime or whether it is divisible by other numbers. In most cases, it takes only a few seconds to find the smallest factor other than one.
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Instructions
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Look at the last integer in your number to determine whether it is even or odd. If the number ends in 0, 2, 4, 6 or 8, the number is even, and divisible by 2. 322, 907890, 12 and 4 are all examples of even numbers. All other numbers are odd. Odd numbers are not divisible by any other even numbers such as 4, 6 or 8.
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Add up the integers in your number to determine whether it is divisible by 3. If the integers add up to a multi-digit number, add the integers in that number together until you get a single-digit sum. If the integers add up to the single digit 3, 6 or 9, the number is divisible by 3. If the integers add up to any other number, the number is not divisible by 3.
For example, in the number 30, 3+0 = 3. In the number 18, 1+8 = 9. These numbers are divisible by 3.
99 is also divisible by 3, but 9+9 = 18, a two digit number. Add the integers 1+8 together to get 9, a number divisible by 3.
If your number is not divisible by 3, it is also not divisible by 9, 21 or any other numbers divisible by 3.
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3
Look at the last integer in your number to determine whether it is divisible by 5 (skip 4, because if you ruled out the number being divisible by 2, it can't be divisible by 4). If the last integer is 5, the number is divisible by 5. Only numbers that end in 0 and 5 are divisible by 5. If your number isn't divisible by 2, 3 or 5, test it to see whether or not it is prime.
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Calculate the square root of your number and round up to the nearest integer. For example, if your number is 127, its square root is about 11.27, which rounds up to 12.
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Make a list of all the prime numbers from 2, the smallest prime number, to the integer calculated in the last step. For our example, the prime numbers from 2 to 12 are 2, 3, 5, 7 and 11.
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Divide your number by each of these prime numbers. You can make the problem easier by ruling out 2, 3 and 5, which you already ruled out in previous steps. For the example, 127 is not divisible by 7 or 11, so it must be prime. If your number is divisible by one of the prime numbers, the first divisible number is your smallest factor other than 1.
Some more examples:
49 is not divisible by 2, 3, or 5. The square root of 49 is 7. Therefore, the smallest factor other than 1 = 7.
143 is not divisible by 2, 3 or 5. The square root of 143 rounds up to 12. The prime numbers from 2 to 12 are 2, 3, 5, 7 and 11. 143/7 = 20.43, so it is not divisible by 7. 143/11 = 13. The smallest factor of 143, other than 1, is 13.
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References
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