FactorsAbout 15
A quarter of an hour is 15 minutes. 15 is the product of the two smallest odd primes, 3 and 5.
Factor pairs of 15
A factor pair is two numbers that multiply to give 15: 1 × 15 and 3 × 5. Each pair is a way of arranging 15 things in equal rows, so 15 tiles can be laid out as a rectangle in 2 different shapes.
How to find the factors of 15 by hand
Divide 15 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 3, because the next number, 4, gives 4 × 4 = 16, which is more than 15: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 15? | Result |
|---|---|---|
| 1 | yes | 1 × 15 |
| 2 | no | remainder 1 |
| 3 | yes | 3 × 5 |
The only number that fails is 2. All the others give a pair.
Prime factorisation of 15
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 15 = 3 × 5. Its prime factors are 3 and 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (1 + 1) × (1 + 1) = 4. This works because a factor of 15 can use each prime anywhere from zero times up to its full power.
The 4 factors add up to 24. Leaving out 15 itself, the rest add up to 9, which is less than 15, so 15 is a deficient number. Of its factors, 4 are odd: 1, 3, 5 and 15.
Divisibility rules applied to 15
The quick tests agree with the factor list above.
- By 2: no. The last digit is 5, which is odd.
- By 3: yes. The digits add up to 1 + 5 = 6, which is a multiple of 3.
- By 4: no. The last two digits make 15, and 15 ÷ 4 leaves remainder 3.
- By 5: yes. The last digit is 5.
- By 6: no. A number divides by 6 when it divides by both 2 and 3. Here the test for 2 fails.
- By 8: no. 15 ÷ 8 leaves remainder 7.
- 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 5 and 1. Their difference is 4, which is not 0 or a multiple of 11.
HCF and LCM with 15
15 and 12. 15 = 3 × 5 and 12 = 22 × 3. The primes they share, each with its smaller power, give the HCF: 3. Every prime with its larger power gives the LCM: 60. By division: 15 = 12 × 1 + 3; 12 = 3 × 4 + 0, so the last divisor, 3, is the HCF. Check: 3 × 60 = 180 = 15 × 12.
15 and 16. 15 = 3 × 5 and 16 = 24. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 240. By division: 16 = 15 × 1 + 1; 15 = 1 × 15 + 0, so the last divisor, 1, is the HCF. Check: 1 × 240 = 240 = 15 × 16.
Multiples of 15
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135 and 150. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 15?
The factors of 15 are 1, 3, 5 and 15. There are 4 of them.
What is the prime factorisation of 15?
15 = 3 × 5.
Is 15 a perfect square?
No. 3 × 3 = 9 and 4 × 4 = 16, and 15 lies between them.
What is the greatest factor of 15 other than itself?
5. Divide 15 by its smallest prime factor, 3, to get it.