Factors of 625: Pairs, Prime Factors and Working

About 625

625 is 25 × 25 and also 5 × 5 × 5 × 5. As the fourth power of a prime it has exactly five factors.

Factor pairs of 625

A factor pair is two numbers that multiply to give 625: 1 × 625, 5 × 125 and 25 × 25. Each pair is a way of arranging 625 things in equal rows, so 625 tiles can be laid out as a rectangle in 3 different shapes, one of them a square of side 25.

How to find the factors of 625 by hand

Divide 625 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 25, because 25 × 25 is exactly 625: any larger factor has already turned up as the partner of a smaller one.

Try	Divides 625?	Result
1	yes	1 × 625
2	no	remainder 1
3	no	remainder 1
4	no	remainder 1
5	yes	5 × 125
6	no	remainder 1
7	no	remainder 2
8	no	remainder 1
9	no	remainder 4
10	no	remainder 5
11	no	remainder 9
12	no	remainder 1
13	no	remainder 1
14	no	remainder 9
15	no	remainder 10
16	no	remainder 1
17	no	remainder 13
18	no	remainder 13
19	no	remainder 17
20	no	remainder 5
21	no	remainder 16
22	no	remainder 9
23	no	remainder 4
24	no	remainder 1
25	yes	25 × 25

The numbers that fail are 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and 24. All the others give a pair.

Prime factorisation of 625

Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.

5625

5125

525

Reading down the left side: 625 = 5 × 5 × 5 × 5, which is written 5⁴ 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: (4 + 1) = 5. This works because a factor of 625 can use each prime anywhere from zero times up to its full power.

The 5 factors add up to 781. Leaving out 625 itself, the rest add up to 156, which is less than 625, so 625 is a deficient number. Of its factors, 5 are odd: 1, 5, 25, 125 and 625.

Divisibility rules applied to 625

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 6 + 2 + 5 = 13, 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. 625 ÷ 8 leaves remainder 1.
By 9: no. The digits add up to 13, 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 11 and 2. Their difference is 9, which is not 0 or a multiple of 11.

HCF and LCM with 625

625 and 500. 625 = 5⁴ and 500 = 2² × 5³. The primes they share, each with its smaller power, give the HCF: 125. Every prime with its larger power gives the LCM: 2500. By division: 625 = 500 × 1 + 125; 500 = 125 × 4 + 0, so the last divisor, 125, is the HCF. Check: 125 × 2500 = 312500 = 625 × 500.

625 and 720. 625 = 5⁴ and 720 = 2⁴ × 3² × 5. The primes they share, each with its smaller power, give the HCF: 5. Every prime with its larger power gives the LCM: 90000. By division: 720 = 625 × 1 + 95; 625 = 95 × 6 + 55; 95 = 55 × 1 + 40; 55 = 40 × 1 + 15; 40 = 15 × 2 + 10; 15 = 10 × 1 + 5; 10 = 5 × 2 + 0, so the last divisor, 5, is the HCF. Check: 5 × 90000 = 450000 = 625 × 720.

Multiples of 625

Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 625 are 625, 1250, 1875, 2500, 3125, 3750, 4375, 5000, 5625 and 6250. A number has a fixed count of factors but endless multiples.

Common questions

What are the factors of 625?

The factors of 625 are 1, 5, 25, 125 and 625. There are 5 of them.

What is the prime factorisation of 625?

625 = 5 × 5 × 5 × 5.

Is 625 a perfect square?

Yes. 625 = 25 × 25, so its square root is 25.

What is the greatest factor of 625 other than itself?

125. Divide 625 by its smallest prime factor, 5, to get it.

← Factors of 500 Factors of 720 →HCF and LCM calculator Factors of 1 to 100

Factors of 625

The factors of 625