FactorsAbout 300
300 is 3 × 100. Five hours contain 300 minutes.
Factor pairs of 300
A factor pair is two numbers that multiply to give 300: 1 × 300, 2 × 150, 3 × 100, 4 × 75, 5 × 60, 6 × 50, 10 × 30, 12 × 25 and 15 × 20. Each pair is a way of arranging 300 things in equal rows, so 300 tiles can be laid out as a rectangle in 9 different shapes.
How to find the factors of 300 by hand
Divide 300 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 17, because the next number, 18, gives 18 × 18 = 324, which is more than 300: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 300? | Result |
|---|---|---|
| 1 | yes | 1 × 300 |
| 2 | yes | 2 × 150 |
| 3 | yes | 3 × 100 |
| 4 | yes | 4 × 75 |
| 5 | yes | 5 × 60 |
| 6 | yes | 6 × 50 |
| 7 | no | remainder 6 |
| 8 | no | remainder 4 |
| 9 | no | remainder 3 |
| 10 | yes | 10 × 30 |
| 11 | no | remainder 3 |
| 12 | yes | 12 × 25 |
| 13 | no | remainder 1 |
| 14 | no | remainder 6 |
| 15 | yes | 15 × 20 |
| 16 | no | remainder 12 |
| 17 | no | remainder 11 |
The numbers that fail are 7, 8, 9, 11, 13, 14, 16 and 17. All the others give a pair.
Prime factorisation of 300
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 300 = 2 × 2 × 3 × 5 × 5, which is written 22 × 3 × 52 with powers. Its prime factors are 2, 3 and 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (2 + 1) × (1 + 1) × (2 + 1) = 18. This works because a factor of 300 can use each prime anywhere from zero times up to its full power.
The 18 factors add up to 868. Leaving out 300 itself, the rest add up to 568, which is more than 300, so 300 is an abundant number. Of its factors, 6 are odd: 1, 3, 5, 15, 25 and 75.
Divisibility rules applied to 300
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 0, which is even.
- By 3: yes. The digits add up to 3 + 0 + 0 = 3, which is a multiple of 3.
- By 4: yes. The last two digits make 0, and 0 ÷ 4 = 0.
- By 5: yes. The last digit is 0.
- By 6: yes. A number divides by 6 when it divides by both 2 and 3. Here both tests pass.
- By 8: no. 300 ÷ 8 leaves remainder 4.
- By 9: no. The digits add up to 3, 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 3 and 0. Their difference is 3, which is not 0 or a multiple of 11.
HCF and LCM with 300
300 and 256. 300 = 22 × 3 × 52 and 256 = 28. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 19200. By division: 300 = 256 × 1 + 44; 256 = 44 × 5 + 36; 44 = 36 × 1 + 8; 36 = 8 × 4 + 4; 8 = 4 × 2 + 0, so the last divisor, 4, is the HCF. Check: 4 × 19200 = 76800 = 300 × 256.
300 and 360. 300 = 22 × 3 × 52 and 360 = 23 × 32 × 5. The primes they share, each with its smaller power, give the HCF: 60. Every prime with its larger power gives the LCM: 1800. By division: 360 = 300 × 1 + 60; 300 = 60 × 5 + 0, so the last divisor, 60, is the HCF. Check: 60 × 1800 = 108000 = 300 × 360.
Multiples of 300
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 300 are 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 and 3000. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 300?
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300. There are 18 of them.
What is the prime factorisation of 300?
300 = 2 × 2 × 3 × 5 × 5.
Is 300 a perfect square?
No. 17 × 17 = 289 and 18 × 18 = 324, and 300 lies between them.
What is the greatest factor of 300 other than itself?
150. Divide 300 by its smallest prime factor, 2, to get it.