how do you know when you have found all the factors of a numbers?
all the factors are prime.
If any factor is not prime, the it has more factors.
To determine if you have found all the factors of a number, you can follow a step-by-step process:
1. Start by finding the square root of the given number. Let's call it "n."
2. Divide the given number by all the whole numbers starting from 1 up to the square root of "n" (rounded down to the nearest whole number).
3. If a division gives you a whole number quotient with no remainder, both the divisor and quotient are factors of the number.
4. Keep track of all the factors you find.
For example, let's find all the factors of the number 36 using this process:
1. The square root of 36 is 6.
2. Divide 36 by all the whole numbers from 1 to 6: 36 ÷ 1, 36 ÷ 2, 36 ÷ 3, 36 ÷ 4, 36 ÷ 5, and 36 ÷ 6.
3. Determine if each division gives a whole number quotient and no remainder:
- 36 ÷ 1 = 36 (factor pair: 1, 36)
- 36 ÷ 2 = 18 (factor pair: 2, 18)
- 36 ÷ 3 = 12 (factor pair: 3, 12)
- 36 ÷ 4 = 9 (factor pair: 4, 9)
- 36 ÷ 5 = 7.2 (not a factor)
- 36 ÷ 6 = 6 (factor pair: 6, 6)
4. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
By systematically dividing the number by all possible divisors up to the square root of the number, you can find all the factors. If you have checked all the numbers up to the square root and found pairs of factors for each division, you can be confident that you have found all the factors of the given number.