What is the Greatest Common Factor of 42 and 1365?

Greatest common factor (GCF) of 42 and 1365 is 21.

GCF(42,1365) = 21

We will now calculate the prime factors of 42 and 1365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42 and 1365.

How to find the GCF of 42 and 1365?

We will first find the prime factorization of 42 and 1365. After we will calculate the factors of 42 and 1365 and find the biggest common factor number .

Step-1: Prime Factorization of 42

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

42 = 2¹ × 3¹ × 7¹

Step-2: Prime Factorization of 1365

Prime factors of 1365 are 3, 5, 7, 13. Prime factorization of 1365 in exponential form is:

1365 = 3¹ × 5¹ × 7¹ × 13¹

Step-3: Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21

Step-4: Factors of 1365

List of positive integer factors of 1365 that divides 42 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42 and 1365. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 1365 is 21.

Also check out the Least Common Multiple of 42 and 1365