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 54, 58 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 54 and 58 is 2.
GCF(54,58) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 54
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:
54 = 21×33
Prime Factorization of 58
2 | 58 |
29 | 29 |
1 |
Prime factors of 58 are 2,29. Prime factorization of 58 in exponential form is:
58 = 21×291
∴ So by taking common prime factors GCF of 54 and 58 is 2
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 58
List of positive integer factors of 58 that divides 58 without a remainder.
1,2,29,58
Greatest Common Factor
We found the factors and prime factorization of 54 and 58. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 58 is 2.
Also check out the Least Common Multiple of 54 and 58
(i) The GCF of 54 and 58 is associative
GCF of 54 and 58 = GCF of 58 and 54
1. What is the GCF of 54 and 58?
Answer: GCF of 54 and 58 is 2.
2. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
3. What are the Factors of 58?
Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.
4. How to Find the GCF of 54 and 58?
Answer:
Greatest Common Factor of 54 and 58 = 2
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 58
58 = 2 x 29
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2
Step 4: Therefore, the greatest common factor of 54 and 58 is 2