What is the Greatest Common Factor of 1465 and 1470?

Greatest common factor (GCF) of 1465 and 1470 is 5.

GCF(1465,1470) = 5

We will now calculate the prime factors of 1465 and 1470, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1465 and 1470.

How to find the GCF of 1465 and 1470?

We will first find the prime factorization of 1465 and 1470. After we will calculate the factors of 1465 and 1470 and find the biggest common factor number .

Step-1: Prime Factorization of 1465

Prime factors of 1465 are 5, 293. Prime factorization of 1465 in exponential form is:

1465 = 5¹ × 293¹

Step-2: Prime Factorization of 1470

Prime factors of 1470 are 2, 3, 5, 7. Prime factorization of 1470 in exponential form is:

1470 = 2¹ × 3¹ × 5¹ × 7²

Step-3: Factors of 1465

List of positive integer factors of 1465 that divides 1465 without a remainder.

1, 5, 293

Step-4: Factors of 1470

List of positive integer factors of 1470 that divides 1465 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1465 and 1470. The biggest common factor number is the GCF number.
So the greatest common factor 1465 and 1470 is 5.

Also check out the Least Common Multiple of 1465 and 1470