What is the Greatest Common Factor of 3414 and 3430?

Greatest common factor (GCF) of 3414 and 3430 is 2.

GCF(3414,3430) = 2

We will now calculate the prime factors of 3414 and 3430, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3414 and 3430.

How to find the GCF of 3414 and 3430?

We will first find the prime factorization of 3414 and 3430. After we will calculate the factors of 3414 and 3430 and find the biggest common factor number .

Step-1: Prime Factorization of 3414

Prime factors of 3414 are 2, 3, 569. Prime factorization of 3414 in exponential form is:

3414 = 2¹ × 3¹ × 569¹

Step-2: Prime Factorization of 3430

Prime factors of 3430 are 2, 5, 7. Prime factorization of 3430 in exponential form is:

3430 = 2¹ × 5¹ × 7³

Step-3: Factors of 3414

List of positive integer factors of 3414 that divides 3414 without a remainder.

1, 2, 3, 6, 569, 1138, 1707

Step-4: Factors of 3430

List of positive integer factors of 3430 that divides 3414 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3414 and 3430. The biggest common factor number is the GCF number.
So the greatest common factor 3414 and 3430 is 2.

Also check out the Least Common Multiple of 3414 and 3430