How to Find GCF of 782/52, 154/8412?

GCF of 782/52, 154/8412

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 782/52, 154/8412 i.e 2/109356 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/52, 154/8412.

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 782/52,154/8412?

Given fractions are 782/52,154/8412

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 782/52,154/8412, numerators are 782,154

Denominators are 52,8412

The GCF of 782,154 is 2 .

LCM of 52,8412 is 109356.

The greatest common factor of 782/52,154/8412 = [GCF of 782,154]/[LCM of 52,8412]= 2/109356

Therefore, the GCF of 782/52,154/8412 is 2/109356.

Greatest Common Factor of 782,154

To find the highest common factor of 782,154, we have to find the factors of both numbers and list the highest common factor.

The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The HCF of 782,154 is 2.

Lets's calculate GCF of 782,154

Greatest Common Factor (GCF) of 782,154 By Common Division

2	782, 154
	391, 77

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

Greatest Common Factor of 782,154 By Matching Biggest Common Factor Method

Now, list down the factors of 782

1,2,17,23,34,46,391,782

Now, list down the factors of 154

1,2,7,11,14,22,77,154

Greatest Common Factor

We found the factors 782,154 . The biggest common factor number is the GCF number.
So the greatest common factor 782,154 is 2.

Lets's calculate LCM of 52,8412

Lowest Common Multiple of 52,8412 using Common Division

2	52, 8412
2	26, 4206
	13, 2103

∴ So the LCM of the given numbers is 2 x 2 x 13 x 2103 = 109356

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/109356

Therefore, the GCF of Fractions 782/52,154/8412 is 2/109356

Least Common Multiple of 52,8412 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 52,8412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,8412) = 4

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

GCF(52,8412) x common factors =4 x 1 = 4

LCM(52,8412) = ( 52 × 8412 ) / 4

LCM(52,8412) = 437424 / 4

LCM(52,8412) = 109356

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FAQs on GCF of Fractions of 782/52, 154/8412

1. What is the HCF of 782,154?

The HCF of 782,154 is 2

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 782/52, 154/8412?

Answer: GCF of Numerators as per given numbers 782/52, 154/8412 is

GCF of Numerators i.e. for 782,154 is 2

LCM of denominators i.e. for 52,8412 is 109356.

Thus, GCF of Fractions is 2/109356.Finally, GCF of Fractions for 782/52, 154/8412 is 2/109356.