How to Find GCF of 672/51, 312/7672?

GCF of 672/51, 312/7672

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 672/51, 312/7672 i.e 24/391272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 672/51, 312/7672.

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 672/51,312/7672?

Given fractions are 672/51,312/7672

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 672/51,312/7672, numerators are 672,312

Denominators are 51,7672

The GCF of 672,312 is 24 .

LCM of 51,7672 is 391272.

The greatest common factor of 672/51,312/7672 = [GCF of 672,312]/[LCM of 51,7672]= 24/391272

Therefore, the GCF of 672/51,312/7672 is 24/391272.

Greatest Common Factor of 672,312

To find the highest common factor of 672,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 672,312 is 24.

Lets's calculate GCF of 672,312

Greatest Common Factor (GCF) of 672,312 By Common Division

2	672, 312
2	336, 156
2	168, 78
3	84, 39
	28, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 672,312 By Matching Biggest Common Factor Method

Now, list down the factors of 672

1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 672,312 . The biggest common factor number is the GCF number.
So the greatest common factor 672,312 is 24.

Lets's calculate LCM of 51,7672

Lowest Common Multiple of 51,7672 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 391272

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/391272

Therefore, the GCF of Fractions 672/51,312/7672 is 24/391272

Least Common Multiple of 51,7672 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 51,7672 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,7672) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(51,7672) x common factors =1 x 1 = 1

LCM(51,7672) = ( 51 × 7672 ) / 1

LCM(51,7672) = 391272 / 1

LCM(51,7672) = 391272

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FAQs on GCF of Fractions of 672/51, 312/7672

1. What is the HCF of 672,312?

The HCF of 672,312 is 24

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 672/51, 312/7672?

Answer: GCF of Numerators as per given numbers 672/51, 312/7672 is

GCF of Numerators i.e. for 672,312 is 24

LCM of denominators i.e. for 51,7672 is 391272.

Thus, GCF of Fractions is 24/391272.Finally, GCF of Fractions for 672/51, 312/7672 is 24/391272.