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 36, 52 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 36 and 52 is 4.
GCF(36,52) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 36
2 | 36 |
2 | 18 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 36 are 2,3. Prime factorization of 36 in exponential form is:
36 = 22×32
Prime Factorization of 52
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:
52 = 22×131
∴ So by taking common prime factors GCF of 36 and 52 is 4
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1,2,4,13,26,52
Greatest Common Factor
We found the factors and prime factorization of 36 and 52. The biggest common factor number is the GCF number.
So the greatest common factor 36 and 52 is 4.
Also check out the Least Common Multiple of 36 and 52
(i) The GCF of 36 and 52 is associative
GCF of 36 and 52 = GCF of 52 and 36
1. What is the GCF of 36 and 52?
Answer: GCF of 36 and 52 is 4.
2. What are the Factors of 36?
Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.
3. What are the Factors of 52?
Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.
4. How to Find the GCF of 36 and 52?
Answer:
Greatest Common Factor of 36 and 52 = 4
Step 1: Find the prime factorization of 36
36 = 2 x 2 x 3 x 3
Step 2: Find the prime factorization of 52
52 = 2 x 2 x 13
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 2 = 4
Step 4: Therefore, the greatest common factor of 36 and 52 is 4