What is the Greatest Common Factor of 71900 and 71904?

Greatest common factor (GCF) of 71900 and 71904 is 4.

GCF(71900,71904) = 4

We will now calculate the prime factors of 71900 and 71904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71900 and 71904.

How to find the GCF of 71900 and 71904?

We will first find the prime factorization of 71900 and 71904. After we will calculate the factors of 71900 and 71904 and find the biggest common factor number .

Step-1: Prime Factorization of 71900

Prime factors of 71900 are 2, 5, 719. Prime factorization of 71900 in exponential form is:

71900 = 2² × 5² × 719¹

Step-2: Prime Factorization of 71904

Prime factors of 71904 are 2, 3, 7, 107. Prime factorization of 71904 in exponential form is:

71904 = 2⁵ × 3¹ × 7¹ × 107¹

Step-3: Factors of 71900

List of positive integer factors of 71900 that divides 71900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 719, 1438, 2876, 3595, 7190, 14380, 17975, 35950

Step-4: Factors of 71904

List of positive integer factors of 71904 that divides 71900 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 107, 112, 168, 214, 224, 321, 336, 428, 642, 672, 749, 856, 1284, 1498, 1712, 2247, 2568, 2996, 3424, 4494, 5136, 5992, 8988, 10272, 11984, 17976, 23968, 35952

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71900 and 71904. The biggest common factor number is the GCF number.
So the greatest common factor 71900 and 71904 is 4.

Also check out the Least Common Multiple of 71900 and 71904