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    GCF of 120 and 210 (Greatest Common Factor)

    "Greatest Common Factor" Calculator
    Greatest Common Factor of
    and

    What is the Greatest Common Divisor of 120 and 210?

    Answer

    GCF of 120 and 210 is
    30

    (Thirty)

    Finding GCF for 120 and 210 using all factors (divisors) listing

    The first method to find GCF for numbers 120 and 210 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 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

    So the Greatest Common Factor for 120 and 210 is 30

    Finding GCF for 120 and 210 by Prime Factorization

    The second method to find GCF for numbers 120 and 210 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 210: 2, 3, 5, 7

    As we can see there are Prime Factors common to both numbers: 2, 3, 5

    Now we need to multiply them to find GCF: 2 × 3 × 5 = 30

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    What is the GCF of 120 and 210. The GCF of 120 and 210 is 30 — the biggest number that can divide both integers. Step-by-step GCF (GCD) calculation by factoring.
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    GCF Table

    Number 1Number 2GCF
    12019515
    1201964
    1201971
    1201986
    1201991
    12020040
    1202013
    1202022
    1202031
    12020412
    1202055
    1202062
    1202073
    1202088
    1202091
    12021030
    1202111
    1202124
    1202133
    1202142
    1202155
    12021624
    1202171
    1202182
    1202193
    12022020
    1202211
    1202226
    1202231
    1202248

    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 210? (The answer is: 30). Select the first number (e.g. '120') and the second number (e.g. '210'). 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

    FAQ

    What is the Greatest Common Divisor of 120 and 210?

    GCF of 120 and 210 is 30

    How to find the GCF of 120 and 210?

    You can find the GCF of 120 and 210 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 210 is 30.

    What prime factors do 120 and 210 share?

    The prime factorizations of 120 and 210 have 2 × 3 × 5 in common, and multiplying those shared primes gives 30 — exactly the greatest common factor.

    How does the GCF reduce the fraction 120/210?

    Divide the numerator and the denominator by the GCF 30: 120 ÷ 30 = 4 and 210 ÷ 30 = 7. So 120/210 in lowest terms is 4/7.

    See Also