What is the Greatest Common Factor of 41998 and 42009?

Greatest common factor (GCF) of 41998 and 42009 is 11.

GCF(41998,42009) = 11

We will now calculate the prime factors of 41998 and 42009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41998 and 42009.

How to find the GCF of 41998 and 42009?

We will first find the prime factorization of 41998 and 42009. After we will calculate the factors of 41998 and 42009 and find the biggest common factor number .

Step-1: Prime Factorization of 41998

Prime factors of 41998 are 2, 11, 23, 83. Prime factorization of 41998 in exponential form is:

41998 = 2¹ × 11¹ × 23¹ × 83¹

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 41998

List of positive integer factors of 41998 that divides 41998 without a remainder.

1, 2, 11, 22, 23, 46, 83, 166, 253, 506, 913, 1826, 1909, 3818, 20999

Step-4: Factors of 42009

List of positive integer factors of 42009 that divides 41998 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 41998 and 42009. The biggest common factor number is the GCF number.
So the greatest common factor 41998 and 42009 is 11.

Also check out the Least Common Multiple of 41998 and 42009