GCF for 45, 60 and 75
"Greatest Common Factor of 3 Numbers" Calculator
What's the Greatest Common Factor (GCF) of 45, 60 and 75?
Answer
GCF of 45, 60 and 75 is
15
Common factors: 1, 3, 5, 15
15 divides all three: 45 ÷ 15 = 3, 60 ÷ 15 = 4, 75 ÷ 15 = 5 — and 3, 4 and 5 have no factor but 1 common to all of them, so no larger number divides all three.
45 = 32 × 5
60 = 22 × 3 × 5
75 = 3 × 52
| Prime | 45 | 60 | 75 | Lowest power |
|---|---|---|---|---|
| 2 | — | 22 | — | — |
| 3 | 32 | 3 | 3 | 3 |
| 5 | 5 | 5 | 52 | 5 |
— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.
GCF = 3 × 5 = 15
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See Also
- Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
GCF Table
| 1st | 2nd | 3rd | GCF |
|---|---|---|---|
| 45 | 60 | 60 | 15 |
| 45 | 60 | 61 | 1 |
| 45 | 60 | 62 | 1 |
| 45 | 60 | 63 | 3 |
| 45 | 60 | 64 | 1 |
| 45 | 60 | 65 | 5 |
| 45 | 60 | 66 | 3 |
| 45 | 60 | 67 | 1 |
| 45 | 60 | 68 | 1 |
| 45 | 60 | 69 | 3 |
| 45 | 60 | 70 | 5 |
| 45 | 60 | 71 | 1 |
| 45 | 60 | 72 | 3 |
| 45 | 60 | 73 | 1 |
| 45 | 60 | 74 | 1 |
| 45 | 60 | 75 | 15 |
| 45 | 60 | 76 | 1 |
| 45 | 60 | 77 | 1 |
| 45 | 60 | 78 | 3 |
| 45 | 60 | 79 | 1 |
| 45 | 60 | 80 | 5 |
| 45 | 60 | 81 | 3 |
| 45 | 60 | 82 | 1 |
| 45 | 60 | 83 | 1 |
| 45 | 60 | 84 | 3 |
| 45 | 60 | 85 | 5 |
| 45 | 60 | 86 | 1 |
| 45 | 60 | 87 | 3 |
| 45 | 60 | 88 | 1 |
| 45 | 60 | 89 | 1 |
FAQ
What's the Greatest Common Factor (GCF) of 45, 60 and 75?
GCF of 45, 60 and 75 is 15
What prime factors do 45, 60 and 75 share?
All three factorizations contain 3 × 5, and multiplying those shared primes gives 15 — exactly the greatest common factor.
Can you get the GCF of 45, 60 and 75 two numbers at a time?
Yes. The GCF of 45 and 60 is 15, and the GCF of 15 and 75 is 15 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.
How does the GCF simplify the ratio 45 : 60 : 75?
Divide every term by the GCF 15: 45 ÷ 15 = 3, 60 ÷ 15 = 4 and 75 ÷ 15 = 5. So 45 : 60 : 75 in lowest terms is 3 : 4 : 5, and no whole number other than 1 divides all three of those.
See Also
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