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 40, 54 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 40 and 54 is 2.
GCF(40,54) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 40
2 | 40 |
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:
40 = 23×51
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
∴ So by taking common prime factors GCF of 40 and 54 is 2
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors and prime factorization of 40 and 54. The biggest common factor number is the GCF number.
So the greatest common factor 40 and 54 is 2.
Also check out the Least Common Multiple of 40 and 54
(i) The GCF of 40 and 54 is associative
GCF of 40 and 54 = GCF of 54 and 40
1. What is the GCF of 40 and 54?
Answer: GCF of 40 and 54 is 2.
2. What are the Factors of 40?
Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.
3. 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.
4. How to Find the GCF of 40 and 54?
Answer:
Greatest Common Factor of 40 and 54 = 2
Step 1: Find the prime factorization of 40
40 = 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
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 40 and 54 is 2