What is the Greatest Common Factor of 42294 and 42300?

Greatest common factor (GCF) of 42294 and 42300 is 6.

GCF(42294,42300) = 6

We will now calculate the prime factors of 42294 and 42300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42294 and 42300.

How to find the GCF of 42294 and 42300?

We will first find the prime factorization of 42294 and 42300. After we will calculate the factors of 42294 and 42300 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 42300

Prime factors of 42300 are 2, 3, 5, 47. Prime factorization of 42300 in exponential form is:

42300 = 2² × 3² × 5² × 47¹

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 42300

List of positive integer factors of 42300 that divides 42294 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 47, 50, 60, 75, 90, 94, 100, 141, 150, 180, 188, 225, 235, 282, 300, 423, 450, 470, 564, 705, 846, 900, 940, 1175, 1410, 1692, 2115, 2350, 2820, 3525, 4230, 4700, 7050, 8460, 10575, 14100, 21150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42294 and 42300. The biggest common factor number is the GCF number.
So the greatest common factor 42294 and 42300 is 6.

Also check out the Least Common Multiple of 42294 and 42300