What is the Greatest Common Factor of 71189 and 71200?

Greatest common factor (GCF) of 71189 and 71200 is 1.

GCF(71189,71200) = 1

We will now calculate the prime factors of 71189 and 71200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71189 and 71200.

How to find the GCF of 71189 and 71200?

We will first find the prime factorization of 71189 and 71200. After we will calculate the factors of 71189 and 71200 and find the biggest common factor number .

Step-1: Prime Factorization of 71189

Prime factors of 71189 are 257, 277. Prime factorization of 71189 in exponential form is:

71189 = 257¹ × 277¹

Step-2: Prime Factorization of 71200

Prime factors of 71200 are 2, 5, 89. Prime factorization of 71200 in exponential form is:

71200 = 2⁵ × 5² × 89¹

Step-3: Factors of 71189

List of positive integer factors of 71189 that divides 71189 without a remainder.

1, 257, 277

Step-4: Factors of 71200

List of positive integer factors of 71200 that divides 71189 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 89, 100, 160, 178, 200, 356, 400, 445, 712, 800, 890, 1424, 1780, 2225, 2848, 3560, 4450, 7120, 8900, 14240, 17800, 35600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71189 and 71200. The biggest common factor number is the GCF number.
So the greatest common factor 71189 and 71200 is 1.

Also check out the Least Common Multiple of 71189 and 71200