What is the Greatest Common Factor of 10700 and 10705?

Greatest common factor (GCF) of 10700 and 10705 is 5.

GCF(10700,10705) = 5

We will now calculate the prime factors of 10700 and 10705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10700 and 10705.

How to find the GCF of 10700 and 10705?

We will first find the prime factorization of 10700 and 10705. After we will calculate the factors of 10700 and 10705 and find the biggest common factor number .

Step-1: Prime Factorization of 10700

Prime factors of 10700 are 2, 5, 107. Prime factorization of 10700 in exponential form is:

10700 = 2² × 5² × 107¹

Step-2: Prime Factorization of 10705

Prime factors of 10705 are 5, 2141. Prime factorization of 10705 in exponential form is:

10705 = 5¹ × 2141¹

Step-3: Factors of 10700

List of positive integer factors of 10700 that divides 10700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 107, 214, 428, 535, 1070, 2140, 2675, 5350

Step-4: Factors of 10705

List of positive integer factors of 10705 that divides 10700 without a remainder.

1, 5, 2141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10700 and 10705. The biggest common factor number is the GCF number.
So the greatest common factor 10700 and 10705 is 5.

Also check out the Least Common Multiple of 10700 and 10705