List every factor of a whole number, test whether one number divides evenly into another, and use the shortcut divisibility rules for 2, 5, and 10.
A factor of a whole number divides into it evenly (no remainder). To find all factors, try every whole number starting at 1 and pair it up.
Shortcut — Divisibility Rules (test without dividing all the way):
| Divisible by | Rule | Example |
|---|---|---|
| 2 | Last digit is even (0, 2, 4, 6, or 8) | 48 ✔ (last digit 8); 35 ✘ |
| 5 | Last digit is 0 or 5 | 40 ✔; 35 ✔; 42 ✘ |
| 10 | Last digit is 0 | 80 ✔; 75 ✘ |
1. How many factors does 12 have?
Factors of 12: 1, 2, 3, 4, 6, 12. Count them: that is 6 factors.
2. Is 42 divisible by 2?
The divisibility rule for 2: the last digit must be even. The last digit of 42 is 2, which is even, so yes.
3. What is the largest factor of 12 that is less than 12?
Factors of 12 in order: 1, 2, 3, 4, 6, 12. The largest one below 12 is 6.
4. Which number is NOT divisible by 5?
Divisible by 5 means the last digit is 0 or 5. Check each: 35 (last digit 5 ✔), 50 (last digit 0 ✔), 42 (last digit 2 ✘), 100 (last digit 0 ✔).
5. Is 7 a factor of 28? Type 1 for yes, 0 for no.
28 ÷ 7 = 4 exactly (no remainder), so yes, 7 is a factor of 28. Type 1.
6. How many even factors does 12 have? (Hint: list all factors of 12, then count the even ones.)
Factors of 12: 1, 2, 3, 4, 6, 12. The even ones are 2, 4, 6, 12 — that is 4 even factors.
7. Which number below is divisible by both 2 and 5?
To be divisible by both 2 and 5, the last digit must be 0 (that satisfies both rules). Only 30 ends in 0.