How to Find GCF of 736/340, 672/142?

GCF of 736/340, 672/142

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 736/340, 672/142 i.e 32/24140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 736/340, 672/142.

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 736/340,672/142?

Given fractions are 736/340,672/142

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 736/340,672/142, numerators are 736,672

Denominators are 340,142

The GCF of 736,672 is 32 .

LCM of 340,142 is 24140.

The greatest common factor of 736/340,672/142 = [GCF of 736,672]/[LCM of 340,142]= 32/24140

Therefore, the GCF of 736/340,672/142 is 32/24140.

Greatest Common Factor of 736,672

To find the highest common factor of 736,672, we have to find the factors of both numbers and list the highest common factor.

The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736

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 HCF of 736,672 is 32.

Lets's calculate GCF of 736,672

Greatest Common Factor (GCF) of 736,672 By Common Division

2	736, 672
2	368, 336
2	184, 168
2	92, 84
2	46, 42
	23, 21

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 736,672 By Matching Biggest Common Factor Method

Now, list down the factors of 736

1,2,4,8,16,23,32,46,92,184,368,736

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

Greatest Common Factor

We found the factors 736,672 . The biggest common factor number is the GCF number.
So the greatest common factor 736,672 is 32.

Lets's calculate LCM of 340,142

Lowest Common Multiple of 340,142 using Common Division

2	340, 142
	170, 71

∴ So the LCM of the given numbers is 2 x 170 x 71 = 24140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/24140

Therefore, the GCF of Fractions 736/340,672/142 is 32/24140

Least Common Multiple of 340,142 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 340,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(340,142) = 2

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

GCF(340,142) x common factors =2 x 1 = 2

LCM(340,142) = ( 340 × 142 ) / 2

LCM(340,142) = 48280 / 2

LCM(340,142) = 24140

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FAQs on GCF of Fractions of 736/340, 672/142

1. What is the HCF of 736,672?

The HCF of 736,672 is 32

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 736/340, 672/142?

Answer: GCF of Numerators as per given numbers 736/340, 672/142 is

GCF of Numerators i.e. for 736,672 is 32

LCM of denominators i.e. for 340,142 is 24140.

Thus, GCF of Fractions is 32/24140.Finally, GCF of Fractions for 736/340, 672/142 is 32/24140.