What is the Greatest Common Factor of 42109 and 42126?

Greatest common factor (GCF) of 42109 and 42126 is 17.

GCF(42109,42126) = 17

We will now calculate the prime factors of 42109 and 42126, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42109 and 42126.

How to find the GCF of 42109 and 42126?

We will first find the prime factorization of 42109 and 42126. After we will calculate the factors of 42109 and 42126 and find the biggest common factor number .

Step-1: Prime Factorization of 42109

Prime factors of 42109 are 17, 2477. Prime factorization of 42109 in exponential form is:

42109 = 17¹ × 2477¹

Step-2: Prime Factorization of 42126

Prime factors of 42126 are 2, 3, 7, 17, 59. Prime factorization of 42126 in exponential form is:

42126 = 2¹ × 3¹ × 7¹ × 17¹ × 59¹

Step-3: Factors of 42109

List of positive integer factors of 42109 that divides 42109 without a remainder.

1, 17, 2477

Step-4: Factors of 42126

List of positive integer factors of 42126 that divides 42109 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 59, 102, 118, 119, 177, 238, 354, 357, 413, 714, 826, 1003, 1239, 2006, 2478, 3009, 6018, 7021, 14042, 21063

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42109 and 42126. The biggest common factor number is the GCF number.
So the greatest common factor 42109 and 42126 is 17.

Also check out the Least Common Multiple of 42109 and 42126