What is the Greatest Common Factor of 59214 and 59220?

Greatest common factor (GCF) of 59214 and 59220 is 6.

GCF(59214,59220) = 6

We will now calculate the prime factors of 59214 and 59220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59214 and 59220.

How to find the GCF of 59214 and 59220?

We will first find the prime factorization of 59214 and 59220. After we will calculate the factors of 59214 and 59220 and find the biggest common factor number .

Step-1: Prime Factorization of 59214

Prime factors of 59214 are 2, 3, 71, 139. Prime factorization of 59214 in exponential form is:

59214 = 2¹ × 3¹ × 71¹ × 139¹

Step-2: Prime Factorization of 59220

Prime factors of 59220 are 2, 3, 5, 7, 47. Prime factorization of 59220 in exponential form is:

59220 = 2² × 3² × 5¹ × 7¹ × 47¹

Step-3: Factors of 59214

List of positive integer factors of 59214 that divides 59214 without a remainder.

1, 2, 3, 6, 71, 139, 142, 213, 278, 417, 426, 834, 9869, 19738, 29607

Step-4: Factors of 59220

List of positive integer factors of 59220 that divides 59214 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 47, 60, 63, 70, 84, 90, 94, 105, 126, 140, 141, 180, 188, 210, 235, 252, 282, 315, 329, 420, 423, 470, 564, 630, 658, 705, 846, 940, 987, 1260, 1316, 1410, 1645, 1692, 1974, 2115, 2820, 2961, 3290, 3948, 4230, 4935, 5922, 6580, 8460, 9870, 11844, 14805, 19740, 29610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59214 and 59220. The biggest common factor number is the GCF number.
So the greatest common factor 59214 and 59220 is 6.

Also check out the Least Common Multiple of 59214 and 59220