What is the Greatest Common Factor of 42210 and 42224?

Greatest common factor (GCF) of 42210 and 42224 is 14.

GCF(42210,42224) = 14

We will now calculate the prime factors of 42210 and 42224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42210 and 42224.

How to find the GCF of 42210 and 42224?

We will first find the prime factorization of 42210 and 42224. After we will calculate the factors of 42210 and 42224 and find the biggest common factor number .

Step-1: Prime Factorization of 42210

Prime factors of 42210 are 2, 3, 5, 7, 67. Prime factorization of 42210 in exponential form is:

42210 = 2¹ × 3² × 5¹ × 7¹ × 67¹

Step-2: Prime Factorization of 42224

Prime factors of 42224 are 2, 7, 13, 29. Prime factorization of 42224 in exponential form is:

42224 = 2⁴ × 7¹ × 13¹ × 29¹

Step-3: Factors of 42210

List of positive integer factors of 42210 that divides 42210 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 67, 70, 90, 105, 126, 134, 201, 210, 315, 335, 402, 469, 603, 630, 670, 938, 1005, 1206, 1407, 2010, 2345, 2814, 3015, 4221, 4690, 6030, 7035, 8442, 14070, 21105

Step-4: Factors of 42224

List of positive integer factors of 42224 that divides 42210 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 29, 52, 56, 58, 91, 104, 112, 116, 182, 203, 208, 232, 364, 377, 406, 464, 728, 754, 812, 1456, 1508, 1624, 2639, 3016, 3248, 5278, 6032, 10556, 21112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42210 and 42224. The biggest common factor number is the GCF number.
So the greatest common factor 42210 and 42224 is 14.

Also check out the Least Common Multiple of 42210 and 42224