How to Find GCF of 162/238, 980/357?

GCF of 162/238, 980/357

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 162/238, 980/357 i.e 2/714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/238, 980/357.

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 162/238,980/357?

Given fractions are 162/238,980/357

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 162/238,980/357, numerators are 162,980

Denominators are 238,357

The GCF of 162,980 is 2 .

LCM of 238,357 is 714.

The greatest common factor of 162/238,980/357 = [GCF of 162,980]/[LCM of 238,357]= 2/714

Therefore, the GCF of 162/238,980/357 is 2/714.

Greatest Common Factor of 162,980

To find the highest common factor of 162,980, we have to find the factors of both numbers and list the highest common factor.

The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

The HCF of 162,980 is 2.

Lets's calculate GCF of 162,980

Greatest Common Factor (GCF) of 162,980 By Common Division

2	162, 980
	81, 490

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

Greatest Common Factor of 162,980 By Matching Biggest Common Factor Method

Now, list down the factors of 162

1,2,3,6,9,18,27,54,81,162

Now, list down the factors of 980

1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980

Greatest Common Factor

We found the factors 162,980 . The biggest common factor number is the GCF number.
So the greatest common factor 162,980 is 2.

Lets's calculate LCM of 238,357

Lowest Common Multiple of 238,357 using Common Division

7	238, 357
17	34, 51
	2, 3

∴ So the LCM of the given numbers is 7 x 17 x 2 x 3 = 714

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/714

Therefore, the GCF of Fractions 162/238,980/357 is 2/714

Least Common Multiple of 238,357 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 238,357 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(238,357) = 119

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

GCF(238,357) x common factors =119 x 1 = 119

LCM(238,357) = ( 238 × 357 ) / 119

LCM(238,357) = 84966 / 119

LCM(238,357) = 714

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FAQs on GCF of Fractions of 162/238, 980/357

1. What is the HCF of 162,980?

The HCF of 162,980 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 162/238, 980/357?

Answer: GCF of Numerators as per given numbers 162/238, 980/357 is

GCF of Numerators i.e. for 162,980 is 2

LCM of denominators i.e. for 238,357 is 714.

Thus, GCF of Fractions is 2/714.Finally, GCF of Fractions for 162/238, 980/357 is 2/714.