What is the Greatest Common Factor of 41991 and 42009?

Greatest common factor (GCF) of 41991 and 42009 is 3.

GCF(41991,42009) = 3

We will now calculate the prime factors of 41991 and 42009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41991 and 42009.

How to find the GCF of 41991 and 42009?

We will first find the prime factorization of 41991 and 42009. After we will calculate the factors of 41991 and 42009 and find the biggest common factor number .

Step-1: Prime Factorization of 41991

Prime factors of 41991 are 3, 13997. Prime factorization of 41991 in exponential form is:

41991 = 3¹ × 13997¹

Step-2: Prime Factorization of 42009

Prime factors of 42009 are 3, 11, 19, 67. Prime factorization of 42009 in exponential form is:

42009 = 3¹ × 11¹ × 19¹ × 67¹

Step-3: Factors of 41991

List of positive integer factors of 41991 that divides 41991 without a remainder.

1, 3, 13997

Step-4: Factors of 42009

List of positive integer factors of 42009 that divides 41991 without a remainder.

1, 3, 11, 19, 33, 57, 67, 201, 209, 627, 737, 1273, 2211, 3819, 14003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 41991 and 42009. The biggest common factor number is the GCF number.
So the greatest common factor 41991 and 42009 is 3.

Also check out the Least Common Multiple of 41991 and 42009