FactorsAbout 63
63 is 7 × 9. Nine weeks contain 63 days, and its digits add up to 9.
Factor pairs of 63
A factor pair is two numbers that multiply to give 63: 1 × 63, 3 × 21 and 7 × 9. Each pair is a way of arranging 63 things in equal rows, so 63 tiles can be laid out as a rectangle in 3 different shapes.
How to find the factors of 63 by hand
Divide 63 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 7, because the next number, 8, gives 8 × 8 = 64, which is more than 63: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 63? | Result |
|---|---|---|
| 1 | yes | 1 × 63 |
| 2 | no | remainder 1 |
| 3 | yes | 3 × 21 |
| 4 | no | remainder 3 |
| 5 | no | remainder 3 |
| 6 | no | remainder 3 |
| 7 | yes | 7 × 9 |
The numbers that fail are 2, 4, 5 and 6. All the others give a pair.
Prime factorisation of 63
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 63 = 3 × 3 × 7, which is written 32 × 7 with powers. Its prime factors are 3 and 7.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (2 + 1) × (1 + 1) = 6. This works because a factor of 63 can use each prime anywhere from zero times up to its full power.
The 6 factors add up to 104. Leaving out 63 itself, the rest add up to 41, which is less than 63, so 63 is a deficient number. Of its factors, 6 are odd: 1, 3, 7, 9, 21 and 63.
Divisibility rules applied to 63
The quick tests agree with the factor list above.
- By 2: no. The last digit is 3, which is odd.
- By 3: yes. The digits add up to 6 + 3 = 9, which is a multiple of 3.
- By 4: no. The last two digits make 63, and 63 ÷ 4 leaves remainder 3.
- By 5: no. The last digit is 3, not 0 or 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. 63 ÷ 8 leaves remainder 7.
- By 9: yes. The digits add up to 9, which is a multiple of 9.
- By 10: no. The last digit is not 0.
- By 11: no. Adding alternate digits from the right gives 3 and 6. Their difference is 3, which is not 0 or a multiple of 11.
HCF and LCM with 63
63 and 60. 63 = 32 × 7 and 60 = 22 × 3 × 5. The primes they share, each with its smaller power, give the HCF: 3. Every prime with its larger power gives the LCM: 1260. By division: 63 = 60 × 1 + 3; 60 = 3 × 20 + 0, so the last divisor, 3, is the HCF. Check: 3 × 1260 = 3780 = 63 × 60.
63 and 64. 63 = 32 × 7 and 64 = 26. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 4032. By division: 64 = 63 × 1 + 1; 63 = 1 × 63 + 0, so the last divisor, 1, is the HCF. Check: 1 × 4032 = 4032 = 63 × 64.
Multiples of 63
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567 and 630. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 63?
The factors of 63 are 1, 3, 7, 9, 21 and 63. There are 6 of them.
What is the prime factorisation of 63?
63 = 3 × 3 × 7.
Is 63 a perfect square?
No. 7 × 7 = 49 and 8 × 8 = 64, and 63 lies between them.
What is the greatest factor of 63 other than itself?
21. Divide 63 by its smallest prime factor, 3, to get it.