What is the Greatest Common Factor of 35705 and 35714?

Greatest common factor (GCF) of 35705 and 35714 is 1.

GCF(35705,35714) = 1

We will now calculate the prime factors of 35705 and 35714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35705 and 35714.

How to find the GCF of 35705 and 35714?

We will first find the prime factorization of 35705 and 35714. After we will calculate the factors of 35705 and 35714 and find the biggest common factor number .

Step-1: Prime Factorization of 35705

Prime factors of 35705 are 5, 37, 193. Prime factorization of 35705 in exponential form is:

35705 = 5¹ × 37¹ × 193¹

Step-2: Prime Factorization of 35714

Prime factors of 35714 are 2, 7, 2551. Prime factorization of 35714 in exponential form is:

35714 = 2¹ × 7¹ × 2551¹

Step-3: Factors of 35705

List of positive integer factors of 35705 that divides 35705 without a remainder.

1, 5, 37, 185, 193, 965, 7141

Step-4: Factors of 35714

List of positive integer factors of 35714 that divides 35705 without a remainder.

1, 2, 7, 14, 2551, 5102, 17857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35705 and 35714. The biggest common factor number is the GCF number.
So the greatest common factor 35705 and 35714 is 1.

Also check out the Least Common Multiple of 35705 and 35714