What is the Greatest Common Factor of 30923 and 30940?

Greatest common factor (GCF) of 30923 and 30940 is 17.

GCF(30923,30940) = 17

We will now calculate the prime factors of 30923 and 30940, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30923 and 30940.

How to find the GCF of 30923 and 30940?

We will first find the prime factorization of 30923 and 30940. After we will calculate the factors of 30923 and 30940 and find the biggest common factor number .

Step-1: Prime Factorization of 30923

Prime factors of 30923 are 17, 107. Prime factorization of 30923 in exponential form is:

30923 = 17² × 107¹

Step-2: 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-3: Factors of 30923

List of positive integer factors of 30923 that divides 30923 without a remainder.

1, 17, 107, 289, 1819

Step-4: Factors of 30940

List of positive integer factors of 30940 that divides 30923 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30923 and 30940. The biggest common factor number is the GCF number.
So the greatest common factor 30923 and 30940 is 17.

Also check out the Least Common Multiple of 30923 and 30940