What is the Greatest Common Factor of 71190 and 71200?

Greatest common factor (GCF) of 71190 and 71200 is 10.

GCF(71190,71200) = 10

We will now calculate the prime factors of 71190 and 71200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71190 and 71200.

How to find the GCF of 71190 and 71200?

We will first find the prime factorization of 71190 and 71200. After we will calculate the factors of 71190 and 71200 and find the biggest common factor number .

Step-1: Prime Factorization of 71190

Prime factors of 71190 are 2, 3, 5, 7, 113. Prime factorization of 71190 in exponential form is:

71190 = 2¹ × 3² × 5¹ × 7¹ × 113¹

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 71190

List of positive integer factors of 71190 that divides 71190 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 113, 126, 210, 226, 315, 339, 565, 630, 678, 791, 1017, 1130, 1582, 1695, 2034, 2373, 3390, 3955, 4746, 5085, 7119, 7910, 10170, 11865, 14238, 23730, 35595

Step-4: Factors of 71200

List of positive integer factors of 71200 that divides 71190 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 71190 and 71200. The biggest common factor number is the GCF number.
So the greatest common factor 71190 and 71200 is 10.

Also check out the Least Common Multiple of 71190 and 71200