What is the Greatest Common Factor of 30500 and 30510?

Greatest common factor (GCF) of 30500 and 30510 is 10.

GCF(30500,30510) = 10

We will now calculate the prime factors of 30500 and 30510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30500 and 30510.

How to find the GCF of 30500 and 30510?

We will first find the prime factorization of 30500 and 30510. After we will calculate the factors of 30500 and 30510 and find the biggest common factor number .

Step-1: Prime Factorization of 30500

Prime factors of 30500 are 2, 5, 61. Prime factorization of 30500 in exponential form is:

30500 = 2² × 5³ × 61¹

Step-2: Prime Factorization of 30510

Prime factors of 30510 are 2, 3, 5, 113. Prime factorization of 30510 in exponential form is:

30510 = 2¹ × 3³ × 5¹ × 113¹

Step-3: Factors of 30500

List of positive integer factors of 30500 that divides 30500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 61, 100, 122, 125, 244, 250, 305, 500, 610, 1220, 1525, 3050, 6100, 7625, 15250

Step-4: Factors of 30510

List of positive integer factors of 30510 that divides 30500 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 113, 135, 226, 270, 339, 565, 678, 1017, 1130, 1695, 2034, 3051, 3390, 5085, 6102, 10170, 15255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30500 and 30510. The biggest common factor number is the GCF number.
So the greatest common factor 30500 and 30510 is 10.

Also check out the Least Common Multiple of 30500 and 30510