Two tests that make one
Is 7,240 a multiple of 40? Build a test from two that you know.
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Step 1 of 4
- 40 = 5 × 8. So test 5 and 8.
- Try 4 and 10 on 20. 20 ÷ 4 = 5 and 20 ÷ 10 = 2.
- Both pass. But 20 ÷ 40 is not whole.
- 7,240 passes 5 and 8. And 7,240 = 40 × 181.
The rule
Yes. 7,240 = 40 × 181, and 7,240 passes the tests for 5 and 8.
40 is 2 × 2 × 2 × 5. If 8 divides a number, three 2s are among its factors. If 5 divides a number, a 5 is among its factors. Together they give all of 40. 5 and 8 share no factor except 1. So no 2 is used twice.
4 needs two 2s. 10 needs one 2 and a 5. They can use the same 2. So 20 passes both. But 20 is 2 × 2 × 5, with only two 2s.
Rule: To test 40, check 5 and 8. Checking 4 and 10 is not enough, because 20 passes both.
| Number | Tests 4 and 10 | Tests 5 and 8 | Multiple of 40? |
|---|---|---|---|
| 20 | both pass | 5 passes, 8 fails | no |
| 7,240 | both pass | both pass | yes |