Greatest Common Factor of 42 and 61

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

• Greatest Common Factor of 42 and 61 by prime factorization method
• Greatest Common Factor of 42 and 61 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 61

Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:

61 = 61¹

∴ So by taking common prime factors GCF of 42 and 61 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 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Greatest Common Factor

We found the factors and prime factorization of 42 and 61. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 61 is 1.

Also check out the Least Common Multiple of 42 and 61

(i) The GCF of 42 and 61 is associative

GCF of 42 and 61 = GCF of 61 and 42

1. What is the GCF of 42 and 61?

Answer: GCF of 42 and 61 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 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

4. How to Find the GCF of 42 and 61?

Answer:

Greatest Common Factor of 42 and 61 = 1

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 61

61 = 61

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 61 is 1