What is the Greatest Common Factor of 3570 and 3584?

Greatest common factor (GCF) of 3570 and 3584 is 14.

GCF(3570,3584) = 14

We will now calculate the prime factors of 3570 and 3584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3570 and 3584.

How to find the GCF of 3570 and 3584?

We will first find the prime factorization of 3570 and 3584. After we will calculate the factors of 3570 and 3584 and find the biggest common factor number .

Step-1: Prime Factorization of 3570

Prime factors of 3570 are 2, 3, 5, 7, 17. Prime factorization of 3570 in exponential form is:

3570 = 2¹ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 3584

Prime factors of 3584 are 2, 7. Prime factorization of 3584 in exponential form is:

3584 = 2⁹ × 7¹

Step-3: Factors of 3570

List of positive integer factors of 3570 that divides 3570 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 30, 34, 35, 42, 51, 70, 85, 102, 105, 119, 170, 210, 238, 255, 357, 510, 595, 714, 1190, 1785

Step-4: Factors of 3584

List of positive integer factors of 3584 that divides 3570 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3570 and 3584. The biggest common factor number is the GCF number.
So the greatest common factor 3570 and 3584 is 14.

Also check out the Least Common Multiple of 3570 and 3584