What is the Greatest Common Factor of 30940 and 30954?

Greatest common factor (GCF) of 30940 and 30954 is 14.

GCF(30940,30954) = 14

We will now calculate the prime factors of 30940 and 30954, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30940 and 30954.

How to find the GCF of 30940 and 30954?

We will first find the prime factorization of 30940 and 30954. After we will calculate the factors of 30940 and 30954 and find the biggest common factor number .

Step-1: Prime Factorization of 30940

Prime factors of 30940 are 2, 5, 7, 13, 17. Prime factorization of 30940 in exponential form is:

30940 = 2² × 5¹ × 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 30954

Prime factors of 30954 are 2, 3, 7, 11, 67. Prime factorization of 30954 in exponential form is:

30954 = 2¹ × 3¹ × 7¹ × 11¹ × 67¹

Step-3: Factors of 30940

List of positive integer factors of 30940 that divides 30940 without a remainder.

1, 2, 4, 5, 7, 10, 13, 14, 17, 20, 26, 28, 34, 35, 52, 65, 68, 70, 85, 91, 119, 130, 140, 170, 182, 221, 238, 260, 340, 364, 442, 455, 476, 595, 884, 910, 1105, 1190, 1547, 1820, 2210, 2380, 3094, 4420, 6188, 7735, 15470

Step-4: Factors of 30954

List of positive integer factors of 30954 that divides 30940 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 67, 77, 134, 154, 201, 231, 402, 462, 469, 737, 938, 1407, 1474, 2211, 2814, 4422, 5159, 10318, 15477

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30940 and 30954. The biggest common factor number is the GCF number.
So the greatest common factor 30940 and 30954 is 14.

Also check out the Least Common Multiple of 30940 and 30954