Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 672, 678 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 672 and 678 is 6.
GCF(672,678) = 6
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 672
2 | 672 |
2 | 336 |
2 | 168 |
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 672 are 2,3,7. Prime factorization of 672 in exponential form is:
672 = 25×31×71
Prime Factorization of 678
2 | 678 |
3 | 339 |
113 | 113 |
1 |
Prime factors of 678 are 2,3,113. Prime factorization of 678 in exponential form is:
678 = 21×31×1131
∴ So by taking common prime factors GCF of 672 and 678 is 6
Factors of 672
List of positive integer factors of 672 that divides 672 without a remainder.
1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672
Factors of 678
List of positive integer factors of 678 that divides 678 without a remainder.
1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors and prime factorization of 672 and 678. The biggest common factor number is the GCF number.
So the greatest common factor 672 and 678 is 6.
Also check out the Least Common Multiple of 672 and 678
(i) The GCF of 672 and 678 is associative
GCF of 672 and 678 = GCF of 678 and 672
1. What is the GCF of 672 and 678?
Answer: GCF of 672 and 678 is 6.
2. What are the Factors of 672?
Answer: Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672. There are 24 integers that are factors of 672. The greatest factor of 672 is 672.
3. What are the Factors of 678?
Answer: Factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678. There are 8 integers that are factors of 678. The greatest factor of 678 is 678.
4. How to Find the GCF of 672 and 678?
Answer:
Greatest Common Factor of 672 and 678 = 6
Step 1: Find the prime factorization of 672
672 = 2 x 2 x 2 x 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 678
678 = 2 x 3 x 113
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 672 and 678 is 6