What is the Greatest Common Factor of 10705 and 10710?

Greatest common factor (GCF) of 10705 and 10710 is 5.

GCF(10705,10710) = 5

We will now calculate the prime factors of 10705 and 10710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10705 and 10710.

How to find the GCF of 10705 and 10710?

We will first find the prime factorization of 10705 and 10710. After we will calculate the factors of 10705 and 10710 and find the biggest common factor number .

Step-1: Prime Factorization of 10705

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

10705 = 5¹ × 2141¹

Step-2: Prime Factorization of 10710

Prime factors of 10710 are 2, 3, 5, 7, 17. Prime factorization of 10710 in exponential form is:

10710 = 2¹ × 3² × 5¹ × 7¹ × 17¹

Step-3: Factors of 10705

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

1, 5, 2141

Step-4: Factors of 10710

List of positive integer factors of 10710 that divides 10705 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 17, 18, 21, 30, 34, 35, 42, 45, 51, 63, 70, 85, 90, 102, 105, 119, 126, 153, 170, 210, 238, 255, 306, 315, 357, 510, 595, 630, 714, 765, 1071, 1190, 1530, 1785, 2142, 3570, 5355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10705 and 10710. The biggest common factor number is the GCF number.
So the greatest common factor 10705 and 10710 is 5.

Also check out the Least Common Multiple of 10705 and 10710