GCF of 120 and 168 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 120 and 168?

Answer

GCF of 120 and 168 is
24

(Twenty-four)

Finding GCF for 120 and 168 using all factors (divisors) listing

The first method to find GCF for numbers 120 and 168 is to list all factors for both numbers and pick the highest common one:

All factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

All factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

So the Greatest Common Factor for 120 and 168 is 24

Finding GCF for 120 and 168 by Prime Factorization

The second method to find GCF for numbers 120 and 168 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 120: 2, 2, 2, 3, 5

All Prime Factors of 168: 2, 2, 2, 3, 7

As we can see there are Prime Factors common to both numbers: 2, 2, 2, 3

Now we need to multiply them to find GCF: 2 × 2 × 2 × 3 = 24

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 120 and 168? (The answer is: 24). Select the first number (e.g. '120') and the second number (e.g. '168'). After that hit the 'Calculate' button.
Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.
"Greatest Common Factor" Calculator
Greatest Common Factor of
and

GCF Table

Number 1Number 2GCF
1201533
1201542
1201555
12015612
1201571
1201582
1201593
12016040
1201611
1201626
1201631
1201644
12016515
1201662
1201671
12016824
1201691
12017010
1201713
1201724
1201731
1201746
1201755
1201768
1201773
1201782
1201791
12018060
1201811
1201822

FAQ

What is the Greatest Common Divisor of 120 and 168?

GCF of 120 and 168 is 24

How to find the GCF of 120 and 168?

You can find the GCF of 120 and 168 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 168 is 24.

What prime factors do 120 and 168 share?

The prime factorizations of 120 and 168 have 2 × 2 × 2 × 3 in common, and multiplying those shared primes gives 24 — exactly the greatest common factor.

How does the GCF reduce the fraction 120/168?

Divide the numerator and the denominator by the GCF 24: 120 ÷ 24 = 5 and 168 ÷ 24 = 7. So 120/168 in lowest terms is 5/7.

See Also