How can you quickly find the factors of a number?
Factors are the numbers that divide into another number without leaving a remainder, and can never be bigger than the original number.
To find factors quickly:
- Start with 1 and the original number.
- Begin testing integers from 2 upward.
- If a number divides evenly, add both the divisor and its quotient to your list.
- Stop once your checking number exceeds the square root of the original number.
If you only find two factors (1 and itself), it’s a prime number.
If you find more than two, it’s a composite number.
The largest proper factor (not including the number itself) is simply the biggest number in your list other than the original.
Find Factors of 36
Here’s the step-by-step factorisation of 36:
| Step | Description |
|---|---|
| 1 | Start with 1 and 36 → List: 1, 36 |
| 2 | Try 2: $36 \div 2 = 18$ → ✅ Add 2, 18 → List: 1, 2, 18, 36 |
| 3 | Try 3: $36 \div 3 = 12$ → ✅ Add 3, 12 → List: 1, 2, 3, 12, 18, 36 |
| 4 | Try 4: $36 \div 4 = 9$ → ✅ Add 4, 9 → List: 1, 2, 3, 4, 9, 12, 18, 36 |
| 5 | Try 5: $36 \div 5 = 7.2$ → ❌ Not a factor |
| 6 | Try 6: $36 \div 6 = 6$ → ✅ Add 6 once (no duplicate needed) |
| ✓ | Stop: You’ve reached √36 = 6 |
All factors of 36:
$$ \boxed{1,\ 2,\ 3,\ 4,\ 6,\ 9,\ 12,\ 18,\ 36} $$
- 36 has more than two factors → it is a composite number
- The largest proper factor is 18
Summary
The factors of 36 are all the numbers from 1 to 36 that divide into it without a remainder:
Factors of 36:
$\boxed{1,\ 2,\ 3,\ 4,\ 6,\ 9,\ 12,\ 18,\ 36}$
- If only 1 and the number itself appear, it’s a prime number
- If more than two factors appear, it’s a composite number
Want more practice? Try applying this same method to the factors of 24.