FactorsAbout 16
16 is 2 × 2 × 2 × 2, a power of 2, so every one of its factors is a power of 2 as well. It is also a perfect square, 4 × 4.
Factor pairs of 16
A factor pair is two numbers that multiply to give 16: 1 × 16, 2 × 8 and 4 × 4. Each pair is a way of arranging 16 things in equal rows, so 16 tiles can be laid out as a rectangle in 3 different shapes, one of them a square of side 4.
How to find the factors of 16 by hand
Divide 16 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 4 × 4 is exactly 16: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 16? | Result |
|---|---|---|
| 1 | yes | 1 × 16 |
| 2 | yes | 2 × 8 |
| 3 | no | remainder 1 |
| 4 | yes | 4 × 4 |
The only number that fails is 3. All the others give a pair.
Prime factorisation of 16
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 16 = 2 × 2 × 2 × 2, which is written 24 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: (4 + 1) = 5. This works because a factor of 16 can use each prime anywhere from zero times up to its full power.
The 5 factors add up to 31. Leaving out 16 itself, the rest add up to 15, which is less than 16, so 16 is a deficient number. Of its factors, only one is odd: 1.
Divisibility rules applied to 16
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 1 + 6 = 7, which is not a multiple of 3.
- By 4: yes. The last two digits make 16, and 16 ÷ 4 = 4.
- 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. 16 ÷ 8 = 2.
- By 9: no. The digits add up to 7, 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 1. Their difference is 5, which is not 0 or a multiple of 11.
HCF and LCM with 16
16 and 15. 16 = 24 and 15 = 3 × 5. 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 = 16 × 15.
16 and 18. 16 = 24 and 18 = 2 × 32. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 144. By division: 18 = 16 × 1 + 2; 16 = 2 × 8 + 0, so the last divisor, 2, is the HCF. Check: 2 × 144 = 288 = 16 × 18.
Multiples of 16
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144 and 160. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 16?
The factors of 16 are 1, 2, 4, 8 and 16. There are 5 of them.
What is the prime factorisation of 16?
16 = 2 × 2 × 2 × 2.
Is 16 a perfect square?
Yes. 16 = 4 × 4, so its square root is 4.
What is the greatest factor of 16 other than itself?
8. Divide 16 by its smallest prime factor, 2, to get it.