What is the Greatest Common Factor of 144 and 160?

Greatest common factor (GCF) of 144 and 160 is 16.

GCF(144,160) = 16

We will now calculate the prime factors of 144 and 160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 144 and 160.

How to find the GCF of 144 and 160?

We will first find the prime factorization of 144 and 160. After we will calculate the factors of 144 and 160 and find the biggest common factor number .

Step-1: Prime Factorization of 144

Prime factors of 144 are 2, 3. Prime factorization of 144 in exponential form is:

144 = 2⁴ × 3²

Step-2: Prime Factorization of 160

Prime factors of 160 are 2, 5. Prime factorization of 160 in exponential form is:

160 = 2⁵ × 5¹

Step-3: Factors of 144

List of positive integer factors of 144 that divides 144 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72

Step-4: Factors of 160

List of positive integer factors of 160 that divides 144 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 144 and 160. The biggest common factor number is the GCF number.
So the greatest common factor 144 and 160 is 16.

Also check out the Least Common Multiple of 144 and 160