What is the Greatest Common Factor of 73824 and 73830?

Greatest common factor (GCF) of 73824 and 73830 is 6.

GCF(73824,73830) = 6

We will now calculate the prime factors of 73824 and 73830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73824 and 73830.

How to find the GCF of 73824 and 73830?

We will first find the prime factorization of 73824 and 73830. After we will calculate the factors of 73824 and 73830 and find the biggest common factor number .

Step-1: Prime Factorization of 73824

Prime factors of 73824 are 2, 3, 769. Prime factorization of 73824 in exponential form is:

73824 = 2⁵ × 3¹ × 769¹

Step-2: Prime Factorization of 73830

Prime factors of 73830 are 2, 3, 5, 23, 107. Prime factorization of 73830 in exponential form is:

73830 = 2¹ × 3¹ × 5¹ × 23¹ × 107¹

Step-3: Factors of 73824

List of positive integer factors of 73824 that divides 73824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 769, 1538, 2307, 3076, 4614, 6152, 9228, 12304, 18456, 24608, 36912

Step-4: Factors of 73830

List of positive integer factors of 73830 that divides 73824 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 107, 115, 138, 214, 230, 321, 345, 535, 642, 690, 1070, 1605, 2461, 3210, 4922, 7383, 12305, 14766, 24610, 36915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73824 and 73830. The biggest common factor number is the GCF number.
So the greatest common factor 73824 and 73830 is 6.

Also check out the Least Common Multiple of 73824 and 73830