FactorsAbout 96
96 is 32 × 3 and has twelve factors. Eight dozen is 96.
Factor pairs of 96
A factor pair is two numbers that multiply to give 96: 1 × 96, 2 × 48, 3 × 32, 4 × 24, 6 × 16 and 8 × 12. Each pair is a way of arranging 96 things in equal rows, so 96 tiles can be laid out as a rectangle in 6 different shapes.
How to find the factors of 96 by hand
Divide 96 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 9, because the next number, 10, gives 10 × 10 = 100, which is more than 96: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 96? | Result |
|---|---|---|
| 1 | yes | 1 × 96 |
| 2 | yes | 2 × 48 |
| 3 | yes | 3 × 32 |
| 4 | yes | 4 × 24 |
| 5 | no | remainder 1 |
| 6 | yes | 6 × 16 |
| 7 | no | remainder 5 |
| 8 | yes | 8 × 12 |
| 9 | no | remainder 6 |
The numbers that fail are 5, 7 and 9. All the others give a pair.
Prime factorisation of 96
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 96 = 2 × 2 × 2 × 2 × 2 × 3, which is written 25 × 3 with powers. Its prime factors are 2 and 3.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (5 + 1) × (1 + 1) = 12. This works because a factor of 96 can use each prime anywhere from zero times up to its full power.
The 12 factors add up to 252. Leaving out 96 itself, the rest add up to 156, which is more than 96, so 96 is an abundant number. Of its factors, 2 are odd: 1 and 3.
Divisibility rules applied to 96
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 6, which is even.
- By 3: yes. The digits add up to 9 + 6 = 15, which is a multiple of 3.
- By 4: yes. The last two digits make 96, and 96 ÷ 4 = 24.
- By 5: no. The last digit is 6, not 0 or 5.
- By 6: yes. A number divides by 6 when it divides by both 2 and 3. Here both tests pass.
- By 8: yes. 96 ÷ 8 = 12.
- By 9: no. The digits add up to 15, 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 6 and 9. Their difference is 3, which is not 0 or a multiple of 11.
HCF and LCM with 96
96 and 90. 96 = 25 × 3 and 90 = 2 × 32 × 5. The primes they share, each with its smaller power, give the HCF: 6. Every prime with its larger power gives the LCM: 1440. By division: 96 = 90 × 1 + 6; 90 = 6 × 15 + 0, so the last divisor, 6, is the HCF. Check: 6 × 1440 = 8640 = 96 × 90.
96 and 100. 96 = 25 × 3 and 100 = 22 × 52. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 2400. By division: 100 = 96 × 1 + 4; 96 = 4 × 24 + 0, so the last divisor, 4, is the HCF. Check: 4 × 2400 = 9600 = 96 × 100.
Multiples of 96
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 96 are 96, 192, 288, 384, 480, 576, 672, 768, 864 and 960. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 96?
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. There are 12 of them.
What is the prime factorisation of 96?
96 = 2 × 2 × 2 × 2 × 2 × 3.
Is 96 a perfect square?
No. 9 × 9 = 81 and 10 × 10 = 100, and 96 lies between them.
What is the greatest factor of 96 other than itself?
48. Divide 96 by its smallest prime factor, 2, to get it.