What is the Greatest Common Factor of 75830 and 75840?

Greatest common factor (GCF) of 75830 and 75840 is 10.

GCF(75830,75840) = 10

We will now calculate the prime factors of 75830 and 75840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75830 and 75840.

How to find the GCF of 75830 and 75840?

We will first find the prime factorization of 75830 and 75840. After we will calculate the factors of 75830 and 75840 and find the biggest common factor number .

Step-1: Prime Factorization of 75830

Prime factors of 75830 are 2, 5, 7583. Prime factorization of 75830 in exponential form is:

75830 = 2¹ × 5¹ × 7583¹

Step-2: Prime Factorization of 75840

Prime factors of 75840 are 2, 3, 5, 79. Prime factorization of 75840 in exponential form is:

75840 = 2⁶ × 3¹ × 5¹ × 79¹

Step-3: Factors of 75830

List of positive integer factors of 75830 that divides 75830 without a remainder.

1, 2, 5, 10, 7583, 15166, 37915

Step-4: Factors of 75840

List of positive integer factors of 75840 that divides 75830 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 79, 80, 96, 120, 158, 160, 192, 237, 240, 316, 320, 395, 474, 480, 632, 790, 948, 960, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 5056, 6320, 7584, 9480, 12640, 15168, 18960, 25280, 37920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75830 and 75840. The biggest common factor number is the GCF number.
So the greatest common factor 75830 and 75840 is 10.

Also check out the Least Common Multiple of 75830 and 75840