What is the Greatest Common Factor of 70 and 1365?

Greatest common factor (GCF) of 70 and 1365 is 35.

GCF(70,1365) = 35

We will now calculate the prime factors of 70 and 1365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70 and 1365.

How to find the GCF of 70 and 1365?

We will first find the prime factorization of 70 and 1365. After we will calculate the factors of 70 and 1365 and find the biggest common factor number .

Step-1: Prime Factorization of 70

Prime factors of 70 are 2, 5, 7. Prime factorization of 70 in exponential form is:

70 = 2¹ × 5¹ × 7¹

Step-2: Prime Factorization of 1365

Prime factors of 1365 are 3, 5, 7, 13. Prime factorization of 1365 in exponential form is:

1365 = 3¹ × 5¹ × 7¹ × 13¹

Step-3: Factors of 70

List of positive integer factors of 70 that divides 70 without a remainder.

1, 2, 5, 7, 10, 14, 35

Step-4: Factors of 1365

List of positive integer factors of 1365 that divides 70 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70 and 1365. The biggest common factor number is the GCF number.
So the greatest common factor 70 and 1365 is 35.

Also check out the Least Common Multiple of 70 and 1365