What is the Greatest Common Factor of 35896 and 35910?

Greatest common factor (GCF) of 35896 and 35910 is 14.

GCF(35896,35910) = 14

We will now calculate the prime factors of 35896 and 35910, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35896 and 35910.

How to find the GCF of 35896 and 35910?

We will first find the prime factorization of 35896 and 35910. After we will calculate the factors of 35896 and 35910 and find the biggest common factor number .

Step-1: Prime Factorization of 35896

Prime factors of 35896 are 2, 7, 641. Prime factorization of 35896 in exponential form is:

35896 = 2³ × 7¹ × 641¹

Step-2: Prime Factorization of 35910

Prime factors of 35910 are 2, 3, 5, 7, 19. Prime factorization of 35910 in exponential form is:

35910 = 2¹ × 3³ × 5¹ × 7¹ × 19¹

Step-3: Factors of 35896

List of positive integer factors of 35896 that divides 35896 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 641, 1282, 2564, 4487, 5128, 8974, 17948

Step-4: Factors of 35910

List of positive integer factors of 35910 that divides 35896 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 19, 21, 27, 30, 35, 38, 42, 45, 54, 57, 63, 70, 90, 95, 105, 114, 126, 133, 135, 171, 189, 190, 210, 266, 270, 285, 315, 342, 378, 399, 513, 570, 630, 665, 798, 855, 945, 1026, 1197, 1330, 1710, 1890, 1995, 2394, 2565, 3591, 3990, 5130, 5985, 7182, 11970, 17955

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35896 and 35910. The biggest common factor number is the GCF number.
So the greatest common factor 35896 and 35910 is 14.

Also check out the Least Common Multiple of 35896 and 35910