GCF and LCM · part 3 of 7
Factor Facts
How to tell what divides into a number without dividing.
Factor Facts
When you are staring at a number wondering what splits it, you do not have to guess. Most of the small primes leave a clue in the digits. Each clue has a reason, and the reason is worth more than the clue.
| Divides by | How to tell | Why that works |
|---|---|---|
| 2 | The last digit is even: 0, 2, 4, 6 or 8. | Every ten is even, so all the tens take care of themselves. Only what is left over at the end can spoil it. |
| 5 | The last digit is 0 or 5. | Same reason. Every ten is a multiple of 5, so only the last digit gets a say. |
| 10 | The last digit is 0. | It needs a 2 and a 5, so it needs both of the tests above at once. |
| 3 | Add the digits. If that total divides by 3, so does the number. | Take 51. 5 + 1 = 6, and 3 divides 6, so 3 divides 51. |
| 9 | Add the digits. If that total divides by 9, so does the number. | Take 72. 7 + 2 = 9, and 9 divides 9, so 9 divides 72. |
| 4 | Look at the last two digits only. | 100 divides by 4, so every hundred is already safe. Only the part below 100 can spoil it. |
| 6 | It passes the 2 test and the 3 test. | 6 is 2 x 3, so a number needs both of those inside it. |
| 7 | There is no easy one. Just divide and see. | Honest answer: 7 does not line up with 10 the way 2, 3 and 5 do, so no digit trick falls out. Most people try 2, 3 and 5 first and only reach for 7 when those fail. |
Finn
Take 51. 5 + 1 = 6, and 3 divides 6, so 3 divides 51.