Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 42, 63 i.e. 21 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 42 and 63 is **21**.

GCF(42,63) = 21

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 42 and 63 by prime factorization method
- Greatest Common Factor of 42 and 63 by matching factors method

**Prime Factorization of 42**

2 | 42 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 42 are 2,3,7. Prime factorization of **42** in exponential form is:

42 = 2^{1}×3^{1}×7^{1}

**Prime Factorization of 63**

3 | 63 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 63 are 3,7. Prime factorization of **63** in exponential form is:

63 = 3^{2}×7^{1}

∴ So by taking common prime factors GCF of 42 and 63 is 21

**Factors of 42**

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

**Factors of 63**

List of positive integer factors of 63 that divides 63 without a remainder.

1,3,7,9,21,63

**Greatest Common Factor**

We found the factors and prime factorization of 42 and 63. The biggest common factor number is the **GCF** number.

So the **greatest common factor 42 and 63** is **21**.

Also check out the Least Common Multiple of 42 and 63

(i) The GCF of 42 and 63 is associative

GCF of 42 and 63 = GCF of 63 and 42

1. What is the GCF of 42 and 63?

Answer: GCF of 42 and 63 is 21.

2. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

3. What are the Factors of 63?

Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.

4. How to Find the GCF of 42 and 63?

Answer:

Greatest Common Factor of 42 and 63 = 21

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 63

63 = 3 x 3 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3 x 7 = 21

Step 4: Therefore, the greatest common factor of 42 and 63 is 21