How do you find the factors of a number? - Answers

okay say it was 10 :1.u say 1 goes into 10 10 times so yes2.u say 2 2 goes into 10 5 times so yes3. 3 doesnt go into it evenly so no4. 4 doesnt go into it evenly so no5. 5 goes into it 2ce so yes6. 6 doesnt go into it evenly so no7. 7 doesnt go in evenly so no8. 8 doesnt go into it evenly so no9. 9 doesnt go into it evenly so no10. and last but certainly not least 10 goes into 10 once so yes and the factors are1,2,5,10There 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: 108The prime factorization can be found by using a factor tree.10854,227,2,29,3,2,23,3,3,2,22^2 x 3^3 = 108Half 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 = 12108 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, 108Notice that all of those numbers, except for 1, can also be found in the prime factorization.