Greatest Common Factor of 42 and 53

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

• Greatest Common Factor of 42 and 53 by prime factorization method
• Greatest Common Factor of 42 and 53 by matching factors method

Prime Factorization of 42

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

42 = 2¹×3¹×7¹

Prime Factorization of 53

Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:

53 = 53¹

∴ So by taking common prime factors GCF of 42 and 53 is 1

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 53

List of positive integer factors of 53 that divides 53 without a remainder.

1,53

Greatest Common Factor

We found the factors and prime factorization of 42 and 53. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 53 is 1.

Also check out the Least Common Multiple of 42 and 53

(i) The GCF of 42 and 53 is associative

GCF of 42 and 53 = GCF of 53 and 42

1. What is the GCF of 42 and 53?

Answer: GCF of 42 and 53 is 1.

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 53?

Answer: Factors of 53 are 1, 53. There are 2 integers that are factors of 53. The greatest factor of 53 is 53.

4. How to Find the GCF of 42 and 53?

Answer:

Greatest Common Factor of 42 and 53 = 1

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 53

53 = 53

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 42 and 53 is 1