What is the Greatest Common Factor of 30407 and 30420?

Greatest common factor (GCF) of 30407 and 30420 is 13.

GCF(30407,30420) = 13

We will now calculate the prime factors of 30407 and 30420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30407 and 30420.

How to find the GCF of 30407 and 30420?

We will first find the prime factorization of 30407 and 30420. After we will calculate the factors of 30407 and 30420 and find the biggest common factor number .

Step-1: Prime Factorization of 30407

Prime factors of 30407 are 13, 2339. Prime factorization of 30407 in exponential form is:

30407 = 13¹ × 2339¹

Step-2: Prime Factorization of 30420

Prime factors of 30420 are 2, 3, 5, 13. Prime factorization of 30420 in exponential form is:

30420 = 2² × 3² × 5¹ × 13²

Step-3: Factors of 30407

List of positive integer factors of 30407 that divides 30407 without a remainder.

1, 13, 2339

Step-4: Factors of 30420

List of positive integer factors of 30420 that divides 30407 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 169, 180, 195, 234, 260, 338, 390, 468, 507, 585, 676, 780, 845, 1014, 1170, 1521, 1690, 2028, 2340, 2535, 3042, 3380, 5070, 6084, 7605, 10140, 15210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30407 and 30420. The biggest common factor number is the GCF number.
So the greatest common factor 30407 and 30420 is 13.

Also check out the Least Common Multiple of 30407 and 30420