FactorsAbout 256
256 is 2 multiplied by itself eight times. It is the number of different values that one byte of computer memory can hold.
Factor pairs of 256
A factor pair is two numbers that multiply to give 256: 1 × 256, 2 × 128, 4 × 64, 8 × 32 and 16 × 16. Each pair is a way of arranging 256 things in equal rows, so 256 tiles can be laid out as a rectangle in 5 different shapes, one of them a square of side 16.
How to find the factors of 256 by hand
Divide 256 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 16, because 16 × 16 is exactly 256: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 256? | Result |
|---|---|---|
| 1 | yes | 1 × 256 |
| 2 | yes | 2 × 128 |
| 3 | no | remainder 1 |
| 4 | yes | 4 × 64 |
| 5 | no | remainder 1 |
| 6 | no | remainder 4 |
| 7 | no | remainder 4 |
| 8 | yes | 8 × 32 |
| 9 | no | remainder 4 |
| 10 | no | remainder 6 |
| 11 | no | remainder 3 |
| 12 | no | remainder 4 |
| 13 | no | remainder 9 |
| 14 | no | remainder 4 |
| 15 | no | remainder 1 |
| 16 | yes | 16 × 16 |
The numbers that fail are 3, 5, 6, 7, 9, 10, 11, 12, 13, 14 and 15. All the others give a pair.
Prime factorisation of 256
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, which is written 28 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: (8 + 1) = 9. This works because a factor of 256 can use each prime anywhere from zero times up to its full power.
The 9 factors add up to 511. Leaving out 256 itself, the rest add up to 255, which is less than 256, so 256 is a deficient number. Of its factors, only one is odd: 1.
Divisibility rules applied to 256
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 6, which is even.
- By 3: no. The digits add up to 2 + 5 + 6 = 13, which is not a multiple of 3.
- By 4: yes. The last two digits make 56, and 56 ÷ 4 = 14.
- By 5: no. The last digit is 6, 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. 256 ÷ 8 = 32.
- By 9: no. The digits add up to 13, 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 8 and 5. Their difference is 3, which is not 0 or a multiple of 11.
HCF and LCM with 256
256 and 240. 256 = 28 and 240 = 24 × 3 × 5. The primes they share, each with its smaller power, give the HCF: 16. Every prime with its larger power gives the LCM: 3840. By division: 256 = 240 × 1 + 16; 240 = 16 × 15 + 0, so the last divisor, 16, is the HCF. Check: 16 × 3840 = 61440 = 256 × 240.
256 and 300. 256 = 28 and 300 = 22 × 3 × 52. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 19200. By division: 300 = 256 × 1 + 44; 256 = 44 × 5 + 36; 44 = 36 × 1 + 8; 36 = 8 × 4 + 4; 8 = 4 × 2 + 0, so the last divisor, 4, is the HCF. Check: 4 × 19200 = 76800 = 256 × 300.
Multiples of 256
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 256 are 256, 512, 768, 1024, 1280, 1536, 1792, 2048, 2304 and 2560. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 256?
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256. There are 9 of them.
What is the prime factorisation of 256?
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
Is 256 a perfect square?
Yes. 256 = 16 × 16, so its square root is 16.
What is the greatest factor of 256 other than itself?
128. Divide 256 by its smallest prime factor, 2, to get it.