What is the Greatest Common Factor of 30660 and 30670?

Greatest common factor (GCF) of 30660 and 30670 is 10.

GCF(30660,30670) = 10

We will now calculate the prime factors of 30660 and 30670, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30660 and 30670.

How to find the GCF of 30660 and 30670?

We will first find the prime factorization of 30660 and 30670. After we will calculate the factors of 30660 and 30670 and find the biggest common factor number .

Step-1: Prime Factorization of 30660

Prime factors of 30660 are 2, 3, 5, 7, 73. Prime factorization of 30660 in exponential form is:

30660 = 2² × 3¹ × 5¹ × 7¹ × 73¹

Step-2: Prime Factorization of 30670

Prime factors of 30670 are 2, 5, 3067. Prime factorization of 30670 in exponential form is:

30670 = 2¹ × 5¹ × 3067¹

Step-3: Factors of 30660

List of positive integer factors of 30660 that divides 30660 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 73, 84, 105, 140, 146, 210, 219, 292, 365, 420, 438, 511, 730, 876, 1022, 1095, 1460, 1533, 2044, 2190, 2555, 3066, 4380, 5110, 6132, 7665, 10220, 15330

Step-4: Factors of 30670

List of positive integer factors of 30670 that divides 30660 without a remainder.

1, 2, 5, 10, 3067, 6134, 15335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30660 and 30670. The biggest common factor number is the GCF number.
So the greatest common factor 30660 and 30670 is 10.

Also check out the Least Common Multiple of 30660 and 30670