How to Find GCF of 30/272, 13/964, 684/546?

GCF of 30/272, 13/964, 684/546

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 30/272, 13/964, 684/546 i.e 1/17895696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/272, 13/964, 684/546.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 30/272,13/964,684/546?

Given fractions are 30/272,13/964,684/546

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 30/272,13/964,684/546, numerators are 30,13,684

Denominators are 272,964,546

The GCF of 30,13,684 is 1 .

LCM of 272,964,546 is 17895696.

The greatest common factor of 30/272,13/964,684/546 = [GCF of 30,13,684]/[LCM of 272,964,546]= 1/17895696

Therefore, the GCF of 30/272,13/964,684/546 is 1/17895696.

Greatest Common Factor of 30,13,684

To find the highest common factor of 30,13,684, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 13 are 1, 13

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

The HCF of 30,13,684 is 1.

Lets's calculate GCF of 30,13,684

Greatest Common Factor (GCF) of 30,13,684 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 30,13,684 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 13

1,13

Now, list down the factors of 684

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Greatest Common Factor

We found the factors 30,13,684 . The biggest common factor number is the GCF number.
So the greatest common factor 30,13,684 is 1.

Lets's calculate LCM of 272,964,546

Lowest Common Multiple of 272,964,546 using Common Division

2	272, 964, 546
2	136, 482, 273
	68, 241, 273

∴ So the LCM of the given numbers is 2 x 2 x 68 x 241 x 273 = 17895696

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17895696

Therefore, the GCF of Fractions 30/272,13/964,684/546 is 1/17895696

Least Common Multiple of 272,964,546 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 272,964,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(272,964,546) = 2

common factors(in case of two or more numbers have common factors) = 4

GCF(272,964,546) x common factors =2 x 4 = 8

LCM(272,964,546) = ( 272 × 964 × 546 ) / 8

LCM(272,964,546) = 143165568 / 8

LCM(272,964,546) = 17895696

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/272, 13/964, 684/546

1. What is the HCF of 30,13,684?

The HCF of 30,13,684 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 30/272, 13/964, 684/546?

Answer: GCF of Numerators as per given numbers 30/272, 13/964, 684/546 is

GCF of Numerators i.e. for 30,13,684 is 1

LCM of denominators i.e. for 272,964,546 is 17895696.

Thus, GCF of Fractions is 1/17895696.Finally, GCF of Fractions for 30/272, 13/964, 684/546 is 1/17895696.