GCF for 15, 20 and 42
What's the Greatest Common Factor (GCF) of 15, 20 and 42?
Answer
(One)
1 is the largest positive integer that divides 15, 20 and 42 without a remainder — every other common divisor of the three divides it too.
Finding the GCF of 15, 20 and 42 by Prime Factorization
Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:
All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)
All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)
All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)
| Prime factor | 15 | 20 | 42 | Lowest power |
|---|---|---|---|---|
| 2 | — | 22 | 2 | — |
| 3 | 3 | — | 3 | — |
| 5 | 5 | 5 | — | — |
| 7 | — | — | 7 | — |
Not one prime factor is shared by all three numbers, which makes 15, 20 and 42 relatively prime as a set. The only positive integer dividing all of them is 1.
Checking the GCF of 15, 20 and 42 Two Numbers at a Time
The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.
GCF(a, b, c) = GCF(GCF(a, b), c)
GCF(15, 20) = 5
GCF(5, 42) = 1
GCF(15, 20, 42) = 1
The answer checks out by division — all three quotients come out whole:
15 ÷ 1 = 15
20 ÷ 1 = 20
42 ÷ 1 = 42
15, 20 and 42 have no common factor left — that is what makes 1 the greatest one.
Related Calculations
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
<a href="https://calculat.io/en/number/greatest-common-factor-of-3-numbers/15--20--42">What is the GCF of 15, 20 and 42? - Calculatio</a>
GCF Table
| Number 1 | Number 2 | Number 3 | GCF |
|---|---|---|---|
| 15 | 20 | 27 | 1 |
| 15 | 20 | 28 | 1 |
| 15 | 20 | 29 | 1 |
| 15 | 20 | 30 | 5 |
| 15 | 20 | 31 | 1 |
| 15 | 20 | 32 | 1 |
| 15 | 20 | 33 | 1 |
| 15 | 20 | 34 | 1 |
| 15 | 20 | 35 | 5 |
| 15 | 20 | 36 | 1 |
| 15 | 20 | 37 | 1 |
| 15 | 20 | 38 | 1 |
| 15 | 20 | 39 | 1 |
| 15 | 20 | 40 | 5 |
| 15 | 20 | 41 | 1 |
| 15 | 20 | 42 | 1 |
| 15 | 20 | 43 | 1 |
| 15 | 20 | 44 | 1 |
| 15 | 20 | 45 | 5 |
| 15 | 20 | 46 | 1 |
| 15 | 20 | 47 | 1 |
| 15 | 20 | 48 | 1 |
| 15 | 20 | 49 | 1 |
| 15 | 20 | 50 | 5 |
| 15 | 20 | 51 | 1 |
| 15 | 20 | 52 | 1 |
| 15 | 20 | 53 | 1 |
| 15 | 20 | 54 | 1 |
| 15 | 20 | 55 | 5 |
| 15 | 20 | 56 | 1 |
About "Greatest Common Factor of 3 Numbers" Calculator
The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder