FactorsAbout 25
A quarter of 100. 25 is the square of a prime, so it has exactly three factors. Only squares of primes have exactly three.
Factor pairs of 25
A factor pair is two numbers that multiply to give 25: 1 × 25 and 5 × 5. Each pair is a way of arranging 25 things in equal rows, so 25 tiles can be laid out as a rectangle in 2 different shapes, one of them a square of side 5.
How to find the factors of 25 by hand
Divide 25 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 5, because 5 × 5 is exactly 25: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 25? | Result |
|---|---|---|
| 1 | yes | 1 × 25 |
| 2 | no | remainder 1 |
| 3 | no | remainder 1 |
| 4 | no | remainder 1 |
| 5 | yes | 5 × 5 |
The numbers that fail are 2, 3 and 4. All the others give a pair.
Prime factorisation of 25
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 25 = 5 × 5, which is written 52 with powers. It has only one prime factor, 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (2 + 1) = 3. This works because a factor of 25 can use each prime anywhere from zero times up to its full power.
The 3 factors add up to 31. Leaving out 25 itself, the rest add up to 6, which is less than 25, so 25 is a deficient number. Of its factors, 3 are odd: 1, 5 and 25.
Divisibility rules applied to 25
The quick tests agree with the factor list above.
- By 2: no. The last digit is 5, which is odd.
- By 3: no. The digits add up to 2 + 5 = 7, which is not a multiple of 3.
- By 4: no. The last two digits make 25, and 25 ÷ 4 leaves remainder 1.
- 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. 25 ÷ 8 leaves remainder 1.
- 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 5 and 2. Their difference is 3, which is not 0 or a multiple of 11.
HCF and LCM with 25
25 and 24. 25 = 52 and 24 = 23 × 3. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 600. By division: 25 = 24 × 1 + 1; 24 = 1 × 24 + 0, so the last divisor, 1, is the HCF. Check: 1 × 600 = 600 = 25 × 24.
25 and 28. 25 = 52 and 28 = 22 × 7. The primes they share, each with its smaller power, give the HCF: 1. Every prime with its larger power gives the LCM: 700. By division: 28 = 25 × 1 + 3; 25 = 3 × 8 + 1; 3 = 1 × 3 + 0, so the last divisor, 1, is the HCF. Check: 1 × 700 = 700 = 25 × 28.
Multiples of 25
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 25 are 25, 50, 75, 100, 125, 150, 175, 200, 225 and 250. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 25?
The factors of 25 are 1, 5 and 25. There are 3 of them.
What is the prime factorisation of 25?
25 = 5 × 5.
Is 25 a perfect square?
Yes. 25 = 5 × 5, so its square root is 5.
What is the greatest factor of 25 other than itself?
5. Divide 25 by its smallest prime factor, 5, to get it.