FactorsAbout 80
80 is 16 × 5. Four score is 80.
Factor pairs of 80
A factor pair is two numbers that multiply to give 80: 1 × 80, 2 × 40, 4 × 20, 5 × 16 and 8 × 10. Each pair is a way of arranging 80 things in equal rows, so 80 tiles can be laid out as a rectangle in 5 different shapes.
How to find the factors of 80 by hand
Divide 80 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 8, because the next number, 9, gives 9 × 9 = 81, which is more than 80: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 80? | Result |
|---|---|---|
| 1 | yes | 1 × 80 |
| 2 | yes | 2 × 40 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 20 |
| 5 | yes | 5 × 16 |
| 6 | no | remainder 2 |
| 7 | no | remainder 3 |
| 8 | yes | 8 × 10 |
The numbers that fail are 3, 6 and 7. All the others give a pair.
Prime factorisation of 80
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 80 = 2 × 2 × 2 × 2 × 5, which is written 24 × 5 with powers. Its prime factors are 2 and 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (4 + 1) × (1 + 1) = 10. This works because a factor of 80 can use each prime anywhere from zero times up to its full power.
The 10 factors add up to 186. Leaving out 80 itself, the rest add up to 106, which is more than 80, so 80 is an abundant number. Of its factors, 2 are odd: 1 and 5.
Divisibility rules applied to 80
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 0, which is even.
- By 3: no. The digits add up to 8 + 0 = 8, which is not a multiple of 3.
- By 4: yes. The last two digits make 80, and 80 ÷ 4 = 20.
- By 5: yes. The last digit is 0.
- 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. 80 ÷ 8 = 10.
- By 9: no. The digits add up to 8, which is not a multiple of 9.
- By 10: yes. The last digit is 0.
- By 11: no. Adding alternate digits from the right gives 0 and 8. Their difference is 8, which is not 0 or a multiple of 11.
HCF and LCM with 80
80 and 75. 80 = 24 × 5 and 75 = 3 × 52. The primes they share, each with its smaller power, give the HCF: 5. Every prime with its larger power gives the LCM: 1200. By division: 80 = 75 × 1 + 5; 75 = 5 × 15 + 0, so the last divisor, 5, is the HCF. Check: 5 × 1200 = 6000 = 80 × 75.
80 and 81. 80 = 24 × 5 and 81 = 34. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 6480. By division: 81 = 80 × 1 + 1; 80 = 1 × 80 + 0, so the last divisor, 1, is the HCF. Check: 1 × 6480 = 6480 = 80 × 81.
Multiples of 80
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 80 are 80, 160, 240, 320, 400, 480, 560, 640, 720 and 800. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 80?
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80. There are 10 of them.
What is the prime factorisation of 80?
80 = 2 × 2 × 2 × 2 × 5.
Is 80 a perfect square?
No. 8 × 8 = 64 and 9 × 9 = 81, and 80 lies between them.
What is the greatest factor of 80 other than itself?
40. Divide 80 by its smallest prime factor, 2, to get it.