What is the Greatest Common Factor of 30072 and 30090?

Greatest common factor (GCF) of 30072 and 30090 is 6.

GCF(30072,30090) = 6

We will now calculate the prime factors of 30072 and 30090, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30072 and 30090.

How to find the GCF of 30072 and 30090?

We will first find the prime factorization of 30072 and 30090. After we will calculate the factors of 30072 and 30090 and find the biggest common factor number .

Step-1: Prime Factorization of 30072

Prime factors of 30072 are 2, 3, 7, 179. Prime factorization of 30072 in exponential form is:

30072 = 2³ × 3¹ × 7¹ × 179¹

Step-2: Prime Factorization of 30090

Prime factors of 30090 are 2, 3, 5, 17, 59. Prime factorization of 30090 in exponential form is:

30090 = 2¹ × 3¹ × 5¹ × 17¹ × 59¹

Step-3: Factors of 30072

List of positive integer factors of 30072 that divides 30072 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 179, 358, 537, 716, 1074, 1253, 1432, 2148, 2506, 3759, 4296, 5012, 7518, 10024, 15036

Step-4: Factors of 30090

List of positive integer factors of 30090 that divides 30072 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 59, 85, 102, 118, 170, 177, 255, 295, 354, 510, 590, 885, 1003, 1770, 2006, 3009, 5015, 6018, 10030, 15045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30072 and 30090. The biggest common factor number is the GCF number.
So the greatest common factor 30072 and 30090 is 6.

Also check out the Least Common Multiple of 30072 and 30090