FactorsAbout 32
32 is 2 multiplied by itself five times. Like every power of 2, its only prime factor is 2.
Factor pairs of 32
A factor pair is two numbers that multiply to give 32: 1 × 32, 2 × 16 and 4 × 8. Each pair is a way of arranging 32 things in equal rows, so 32 tiles can be laid out as a rectangle in 3 different shapes.
How to find the factors of 32 by hand
Divide 32 by 1, 2, 3 and so on. Each time the division is exact, you have found two factors at once: the divisor and the answer. You can stop at 5, because the next number, 6, gives 6 × 6 = 36, which is more than 32: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 32? | Result |
|---|---|---|
| 1 | yes | 1 × 32 |
| 2 | yes | 2 × 16 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 8 |
| 5 | no | remainder 2 |
The numbers that fail are 3 and 5. All the others give a pair.
Prime factorisation of 32
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 32 = 2 × 2 × 2 × 2 × 2, which is written 25 with powers. It has only one prime factor, 2.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (5 + 1) = 6. This works because a factor of 32 can use each prime anywhere from zero times up to its full power.
The 6 factors add up to 63. Leaving out 32 itself, the rest add up to 31, which is less than 32, so 32 is a deficient number. Of its factors, only one is odd: 1.
Divisibility rules applied to 32
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 2, which is even.
- By 3: no. The digits add up to 3 + 2 = 5, which is not a multiple of 3.
- By 4: yes. The last two digits make 32, and 32 ÷ 4 = 8.
- By 5: no. The last digit is 2, not 0 or 5.
- By 6: no. A number divides by 6 when it divides by both 2 and 3. Here the test for 3 fails.
- By 8: yes. 32 ÷ 8 = 4.
- By 9: no. The digits add up to 5, which is not a multiple of 9.
- By 10: no. The last digit is not 0.
- By 11: no. Adding alternate digits from the right gives 2 and 3. Their difference is 1, which is not 0 or a multiple of 11.
HCF and LCM with 32
32 and 30. 32 = 25 and 30 = 2 × 3 × 5. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 480. By division: 32 = 30 × 1 + 2; 30 = 2 × 15 + 0, so the last divisor, 2, is the HCF. Check: 2 × 480 = 960 = 32 × 30.
32 and 36. 32 = 25 and 36 = 22 × 32. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 288. By division: 36 = 32 × 1 + 4; 32 = 4 × 8 + 0, so the last divisor, 4, is the HCF. Check: 4 × 288 = 1152 = 32 × 36.
Multiples of 32
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 32 are 32, 64, 96, 128, 160, 192, 224, 256, 288 and 320. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 32?
The factors of 32 are 1, 2, 4, 8, 16 and 32. There are 6 of them.
What is the prime factorisation of 32?
32 = 2 × 2 × 2 × 2 × 2.
Is 32 a perfect square?
No. 5 × 5 = 25 and 6 × 6 = 36, and 32 lies between them.
What is the greatest factor of 32 other than itself?
16. Divide 32 by its smallest prime factor, 2, to get it.