What is the Greatest Common Factor of 42294 and 42309?

Greatest common factor (GCF) of 42294 and 42309 is 3.

GCF(42294,42309) = 3

We will now calculate the prime factors of 42294 and 42309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42294 and 42309.

How to find the GCF of 42294 and 42309?

We will first find the prime factorization of 42294 and 42309. After we will calculate the factors of 42294 and 42309 and find the biggest common factor number .

Step-1: Prime Factorization of 42294

Prime factors of 42294 are 2, 3, 7, 19, 53. Prime factorization of 42294 in exponential form is:

42294 = 2¹ × 3¹ × 7¹ × 19¹ × 53¹

Step-2: Prime Factorization of 42309

Prime factors of 42309 are 3, 1567. Prime factorization of 42309 in exponential form is:

42309 = 3³ × 1567¹

Step-3: Factors of 42294

List of positive integer factors of 42294 that divides 42294 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 53, 57, 106, 114, 133, 159, 266, 318, 371, 399, 742, 798, 1007, 1113, 2014, 2226, 3021, 6042, 7049, 14098, 21147

Step-4: Factors of 42309

List of positive integer factors of 42309 that divides 42294 without a remainder.

1, 3, 9, 27, 1567, 4701, 14103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42294 and 42309. The biggest common factor number is the GCF number.
So the greatest common factor 42294 and 42309 is 3.

Also check out the Least Common Multiple of 42294 and 42309