List the factors of the following number 90. ----------------------------- Let's divide 90 by every integer between 1 and 90 to find out whether or not we get a whole number. If we do, then the integer is a factor of 90; if we don't get a whole number, it isn't. Here goes: 90 ÷ 1 = 90. That's a whole number, so YES, 1 is a factor of 90. SO FAR THE ONLY FACTOR OF 90 WE HAVE FOUND IS: 1 90 ÷ 2 = 45. That's a whole number, so YES, 2 is a factor of 90. SO FAR THAT MAKES 2 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2. 90 ÷ 3 = 30. That's a whole number, so YES, 3 is a factor of 90. SO FAR THAT MAKES 3 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3. 90 ÷ 4 = 22.5. That's NOT a whole number, so NO, 4 is NOT a factor of 90. 90 ÷ 5 = 18. That's a whole number, so YES, 5 is a factor of 90. SO FAR THAT MAKES 4 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5. 90 ÷ 6 = 15. That's a whole number, so YES, 6 is a factor of 90. SO FAR THAT MAKES 5 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6. 90 ÷ 7 = 12.8571429. That's NOT a whole number, so NO, 7 is NOT a factor of 90. 90 ÷ 8 = 11.25. That's NOT a whole number, so NO, 8 is NOT a factor of 90. 90 ÷ 9 = 10. That's a whole number, so YES, 9 is a factor of 90. SO FAR THAT MAKES 6 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9. 90 ÷ 10 = 9. That's a whole number, so YES, 10 is a factor of 90. SO FAR THAT MAKES 7 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10. 90 ÷ 11 = 8.18181818. That's NOT a whole number, so NO, 11 is NOT a factor of 90. 90 ÷ 12 = 7.5. That's NOT a whole number, so NO, 12 is NOT a factor of 90. 90 ÷ 13 = 6.92307692. That's NOT a whole number, so NO, 13 is NOT a factor of 90. 90 ÷ 14 = 6.42857143. That's NOT a whole number, so NO, 14 is NOT a factor of 90. 90 ÷ 15 = 6. That's a whole number, so YES, 15 is a factor of 90. SO FAR THAT MAKES 8 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10, 15. 90 ÷ 16 = 5.625. That's NOT a whole number, so NO, 16 is NOT a factor of 90. 90 ÷ 17 = 5.29411765. That's NOT a whole number, so NO, 17 is NOT a factor of 90. 90 ÷ 18 = 5. That's a whole number, so YES, 18 is a factor of 90. SO FAR THAT MAKES 9 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10, 15, 18. 90 ÷ 19 = 4.73684211. That's NOT a whole number, so NO, 19 is NOT a factor of 90. 90 ÷ 20 = 4.5. That's NOT a whole number, so NO, 20 is NOT a factor of 90. 90 ÷ 21 = 4.28571429. That's NOT a whole number, so NO, 21 is NOT a factor of 90. 90 ÷ 22 = 4.09090909. That's NOT a whole number, so NO, 22 is NOT a factor of 90. 90 ÷ 23 = 3.91304348. That's NOT a whole number, so NO, 23 is NOT a factor of 90. 90 ÷ 24 = 3.75. That's NOT a whole number, so NO, 24 is NOT a factor of 90. 90 ÷ 25 = 3.6. That's NOT a whole number, so NO, 25 is NOT a factor of 90. 90 ÷ 26 = 3.46153846. That's NOT a whole number, so NO, 26 is NOT a factor of 90. 90 ÷ 27 = 3.33333333. That's NOT a whole number, so NO, 27 is NOT a factor of 90. 90 ÷ 28 = 3.21428571. That's NOT a whole number, so NO, 28 is NOT a factor of 90. 90 ÷ 29 = 3.10344828. That's NOT a whole number, so NO, 29 is NOT a factor of 90. 90 ÷ 30 = 3. That's a whole number, so YES, 30 is a factor of 90. SO FAR THAT MAKES 10 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30. 90 ÷ 31 = 2.90322581. That's NOT a whole number, so NO, 31 is NOT a factor of 90. 90 ÷ 32 = 2.8125. That's NOT a whole number, so NO, 32 is NOT a factor of 90. 90 ÷ 33 = 2.72727273. That's NOT a whole number, so NO, 33 is NOT a factor of 90. 90 ÷ 34 = 2.64705882. That's NOT a whole number, so NO, 34 is NOT a factor of 90. 90 ÷ 35 = 2.57142857. That's NOT a whole number, so NO, 35 is NOT a factor of 90. 90 ÷ 36 = 2.5. That's NOT a whole number, so NO, 36 is NOT a factor of 90. 90 ÷ 37 = 2.43243243. That's NOT a whole number, so NO, 37 is NOT a factor of 90. 90 ÷ 38 = 2.36842105. That's NOT a whole number, so NO, 38 is NOT a factor of 90. 90 ÷ 39 = 2.30769231. That's NOT a whole number, so NO, 39 is NOT a factor of 90. 90 ÷ 40 = 2.25. That's NOT a whole number, so NO, 40 is NOT a factor of 90. 90 ÷ 41 = 2.19512195. That's NOT a whole number, so NO, 41 is NOT a factor of 90. 90 ÷ 42 = 2.14285714. That's NOT a whole number, so NO, 42 is NOT a factor of 90. 90 ÷ 43 = 2.09302326. That's NOT a whole number, so NO, 43 is NOT a factor of 90. 90 ÷ 44 = 2.04545455. That's NOT a whole number, so NO, 44 is NOT a factor of 90. 90 ÷ 45 = 2. That's a whole number, so YES, 45 is a factor of 90. SO FAR THAT MAKES 11 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. 90 ÷ 46 = 1.95652174. That's NOT a whole number, so NO, 46 is NOT a factor of 90. 90 ÷ 47 = 1.91489362. That's NOT a whole number, so NO, 47 is NOT a factor of 90. 90 ÷ 48 = 1.875. That's NOT a whole number, so NO, 48 is NOT a factor of 90. 90 ÷ 49 = 1.83673469. That's NOT a whole number, so NO, 49 is NOT a factor of 90. 90 ÷ 50 = 1.8. That's NOT a whole number, so NO, 50 is NOT a factor of 90. 90 ÷ 51 = 1.76470588. That's NOT a whole number, so NO, 51 is NOT a factor of 90. 90 ÷ 52 = 1.73076923. That's NOT a whole number, so NO, 52 is NOT a factor of 90. 90 ÷ 53 = 1.69811321. That's NOT a whole number, so NO, 53 is NOT a factor of 90. 90 ÷ 54 = 1.66666667. That's NOT a whole number, so NO, 54 is NOT a factor of 90. 90 ÷ 55 = 1.63636364. That's NOT a whole number, so NO, 55 is NOT a factor of 90. 90 ÷ 56 = 1.60714286. That's NOT a whole number, so NO, 56 is NOT a factor of 90. 90 ÷ 57 = 1.57894737. That's NOT a whole number, so NO, 57 is NOT a factor of 90. 90 ÷ 58 = 1.55172414. That's NOT a whole number, so NO, 58 is NOT a factor of 90. 90 ÷ 59 = 1.52542373. That's NOT a whole number, so NO, 59 is NOT a factor of 90. 90 ÷ 60 = 1.5. That's NOT a whole number, so NO, 60 is NOT a factor of 90. 90 ÷ 61 = 1.47540984. That's NOT a whole number, so NO, 61 is NOT a factor of 90. 90 ÷ 62 = 1.4516129. That's NOT a whole number, so NO, 62 is NOT a factor of 90. 90 ÷ 63 = 1.42857143. That's NOT a whole number, so NO, 63 is NOT a factor of 90. 90 ÷ 64 = 1.40625. That's NOT a whole number, so NO, 64 is NOT a factor of 90. 90 ÷ 65 = 1.38461538. That's NOT a whole number, so NO, 65 is NOT a factor of 90. 90 ÷ 66 = 1.36363636. That's NOT a whole number, so NO, 66 is NOT a factor of 90. 90 ÷ 67 = 1.34328358. That's NOT a whole number, so NO, 67 is NOT a factor of 90. 90 ÷ 68 = 1.32352941. That's NOT a whole number, so NO, 68 is NOT a factor of 90. 90 ÷ 69 = 1.30434783. That's NOT a whole number, so NO, 69 is NOT a factor of 90. 90 ÷ 70 = 1.28571429. That's NOT a whole number, so NO, 70 is NOT a factor of 90. 90 ÷ 71 = 1.26760563. That's NOT a whole number, so NO, 71 is NOT a factor of 90. 90 ÷ 72 = 1.25. That's NOT a whole number, so NO, 72 is NOT a factor of 90. 90 ÷ 73 = 1.23287671. That's NOT a whole number, so NO, 73 is NOT a factor of 90. 90 ÷ 74 = 1.21621622. That's NOT a whole number, so NO, 74 is NOT a factor of 90. 90 ÷ 75 = 1.2. That's NOT a whole number, so NO, 75 is NOT a factor of 90. 90 ÷ 76 = 1.18421053. That's NOT a whole number, so NO, 76 is NOT a factor of 90. 90 ÷ 77 = 1.16883117. That's NOT a whole number, so NO, 77 is NOT a factor of 90. 90 ÷ 78 = 1.15384615. That's NOT a whole number, so NO, 78 is NOT a factor of 90. 90 ÷ 79 = 1.13924051. That's NOT a whole number, so NO, 79 is NOT a factor of 90. 90 ÷ 80 = 1.125. That's NOT a whole number, so NO, 80 is NOT a factor of 90. 90 ÷ 81 = 1.11111111. That's NOT a whole number, so NO, 81 is NOT a factor of 90. 90 ÷ 82 = 1.09756098. That's NOT a whole number, so NO, 82 is NOT a factor of 90. 90 ÷ 83 = 1.08433735. That's NOT a whole number, so NO, 83 is NOT a factor of 90. 90 ÷ 84 = 1.07142857. That's NOT a whole number, so NO, 84 is NOT a factor of 90. 90 ÷ 85 = 1.05882353. That's NOT a whole number, so NO, 85 is NOT a factor of 90. 90 ÷ 86 = 1.04651163. That's NOT a whole number, so NO, 86 is NOT a factor of 90. 90 ÷ 87 = 1.03448276. That's NOT a whole number, so NO, 87 is NOT a factor of 90. 90 ÷ 88 = 1.02272727. That's NOT a whole number, so NO, 88 is NOT a factor of 90. 90 ÷ 89 = 1.01123596. That's NOT a whole number, so NO, 89 is NOT a factor of 90. 90 ÷ 90 = 1. That's a whole number, so YES, 90 is a factor of 90. SO FAR THAT MAKES 12 FACTORS OF 90. So far all the factors of 90 we've found are these: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. That's all of them. You might look for some shortcuts the next time you are asked for all the factors of an integer. But if you can't think of any shortcuts, then you'll have to go through every possibility as I did above. Edwin