FactorsAbout 24
A day has 24 hours. 24 has more factors than any smaller number, so a day splits evenly into shifts of 2, 3, 4, 6, 8 or 12 hours.
Factor pairs of 24
A factor pair is two numbers that multiply to give 24: 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Each pair is a way of arranging 24 things in equal rows, so 24 tiles can be laid out as a rectangle in 4 different shapes.
How to find the factors of 24 by hand
Divide 24 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 4, because the next number, 5, gives 5 × 5 = 25, which is more than 24: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 24? | Result |
|---|---|---|
| 1 | yes | 1 × 24 |
| 2 | yes | 2 × 12 |
| 3 | yes | 3 × 8 |
| 4 | yes | 4 × 6 |
Every number from 1 to 4 divides 24.
Prime factorisation of 24
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 24 = 2 × 2 × 2 × 3, which is written 23 × 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: (3 + 1) × (1 + 1) = 8. This works because a factor of 24 can use each prime anywhere from zero times up to its full power.
The 8 factors add up to 60. Leaving out 24 itself, the rest add up to 36, which is more than 24, so 24 is an abundant number. Of its factors, 2 are odd: 1 and 3.
Divisibility rules applied to 24
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 4, which is even.
- By 3: yes. The digits add up to 2 + 4 = 6, which is a multiple of 3.
- By 4: yes. The last two digits make 24, and 24 ÷ 4 = 6.
- By 5: no. The last digit is 4, 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. 24 ÷ 8 = 3.
- By 9: no. The digits add up to 6, 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 4 and 2. Their difference is 2, which is not 0 or a multiple of 11.
HCF and LCM with 24
24 and 20. 24 = 23 × 3 and 20 = 22 × 5. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 120. By division: 24 = 20 × 1 + 4; 20 = 4 × 5 + 0, so the last divisor, 4, is the HCF. Check: 4 × 120 = 480 = 24 × 20.
24 and 25. 24 = 23 × 3 and 25 = 52. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 600. By division: 25 = 24 × 1 + 1; 24 = 1 × 24 + 0, so the last divisor, 1, is the HCF. Check: 1 × 600 = 600 = 24 × 25.
Multiples of 24
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 24 are 24, 48, 72, 96, 120, 144, 168, 192, 216 and 240. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 24?
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. There are 8 of them.
What is the prime factorisation of 24?
24 = 2 × 2 × 2 × 3.
Is 24 a perfect square?
No. 4 × 4 = 16 and 5 × 5 = 25, and 24 lies between them.
What is the greatest factor of 24 other than itself?
12. Divide 24 by its smallest prime factor, 2, to get it.