FactorsAbout 50
Half of 100. 50 is twice a square, 2 × 25.
Factor pairs of 50
A factor pair is two numbers that multiply to give 50: 1 × 50, 2 × 25 and 5 × 10. Each pair is a way of arranging 50 things in equal rows, so 50 tiles can be laid out as a rectangle in 3 different shapes.
How to find the factors of 50 by hand
Divide 50 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 50: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 50? | Result |
|---|---|---|
| 1 | yes | 1 × 50 |
| 2 | yes | 2 × 25 |
| 3 | no | remainder 2 |
| 4 | no | remainder 2 |
| 5 | yes | 5 × 10 |
| 6 | no | remainder 2 |
| 7 | no | remainder 1 |
The numbers that fail are 3, 4, 6 and 7. All the others give a pair.
Prime factorisation of 50
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 50 = 2 × 5 × 5, which is written 2 × 52 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: (1 + 1) × (2 + 1) = 6. This works because a factor of 50 can use each prime anywhere from zero times up to its full power.
The 6 factors add up to 93. Leaving out 50 itself, the rest add up to 43, which is less than 50, so 50 is a deficient number. Of its factors, 3 are odd: 1, 5 and 25.
Divisibility rules applied to 50
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 5 + 0 = 5, which is not a multiple of 3.
- By 4: no. The last two digits make 50, and 50 ÷ 4 leaves remainder 2.
- 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: no. 50 ÷ 8 leaves remainder 2.
- By 9: no. The digits add up to 5, 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 5. Their difference is 5, which is not 0 or a multiple of 11.
HCF and LCM with 50
50 and 48. 50 = 2 × 52 and 48 = 24 × 3. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 1200. By division: 50 = 48 × 1 + 2; 48 = 2 × 24 + 0, so the last divisor, 2, is the HCF. Check: 2 × 1200 = 2400 = 50 × 48.
50 and 54. 50 = 2 × 52 and 54 = 2 × 33. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 1350. By division: 54 = 50 × 1 + 4; 50 = 4 × 12 + 2; 4 = 2 × 2 + 0, so the last divisor, 2, is the HCF. Check: 2 × 1350 = 2700 = 50 × 54.
Multiples of 50
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 50 are 50, 100, 150, 200, 250, 300, 350, 400, 450 and 500. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 50?
The factors of 50 are 1, 2, 5, 10, 25 and 50. There are 6 of them.
What is the prime factorisation of 50?
50 = 2 × 5 × 5.
Is 50 a perfect square?
No. 7 × 7 = 49 and 8 × 8 = 64, and 50 lies between them.
What is the greatest factor of 50 other than itself?
25. Divide 50 by its smallest prime factor, 2, to get it.