How to Find GCF of 167/421, 216/978?

GCF of 167/421, 216/978

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 167/421, 216/978 i.e 1/411738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 167/421, 216/978.

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 167/421,216/978?

Given fractions are 167/421,216/978

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 167/421,216/978, numerators are 167,216

Denominators are 421,978

The GCF of 167,216 is 1 .

LCM of 421,978 is 411738.

The greatest common factor of 167/421,216/978 = [GCF of 167,216]/[LCM of 421,978]= 1/411738

Therefore, the GCF of 167/421,216/978 is 1/411738.

Greatest Common Factor of 167,216

To find the highest common factor of 167,216, we have to find the factors of both numbers and list the highest common factor.

The factors of 167 are 1, 167

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The HCF of 167,216 is 1.

Lets's calculate GCF of 167,216

Greatest Common Factor (GCF) of 167,216 By Common Division

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

Greatest Common Factor of 167,216 By Matching Biggest Common Factor Method

Now, list down the factors of 167

1,167

Now, list down the factors of 216

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Greatest Common Factor

We found the factors 167,216 . The biggest common factor number is the GCF number.
So the greatest common factor 167,216 is 1.

Lets's calculate LCM of 421,978

Lowest Common Multiple of 421,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 411738

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/411738

Therefore, the GCF of Fractions 167/421,216/978 is 1/411738

Least Common Multiple of 421,978 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 421,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(421,978) = 1

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

GCF(421,978) x common factors =1 x 1 = 1

LCM(421,978) = ( 421 × 978 ) / 1

LCM(421,978) = 411738 / 1

LCM(421,978) = 411738

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FAQs on GCF of Fractions of 167/421, 216/978

1. What is the HCF of 167,216?

The HCF of 167,216 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 167/421, 216/978?

Answer: GCF of Numerators as per given numbers 167/421, 216/978 is

GCF of Numerators i.e. for 167,216 is 1

LCM of denominators i.e. for 421,978 is 411738.

Thus, GCF of Fractions is 1/411738.Finally, GCF of Fractions for 167/421, 216/978 is 1/411738.