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GCF of 217/364, 1667/412

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 217/364, 1667/412 i.e 1/37492 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/364, 1667/412.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 217/364,1667/412?

Given fractions are 217/364,1667/412

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 217/364,1667/412, numerators are 217,1667

Denominators are 364,412

The GCF of 217,1667 is 1 .

LCM of 364,412 is 37492.

The greatest common factor of 217/364,1667/412 = [GCF of 217,1667]/[LCM of 364,412]= 1/37492

Therefore, the GCF of 217/364,1667/412 is 1/37492.

Greatest Common Factor of 217,1667

To find the highest common factor of 217,1667, we have to find the factors of both numbers and list the highest common factor.

The factors of 217 are 1, 7, 31, 217

The factors of 1667 are 1, 1667

The HCF of 217,1667 is 1.

Lets's calculate GCF of 217,1667

Greatest Common Factor (GCF) of 217,1667 By Common Division

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

Greatest Common Factor of 217,1667 By Matching Biggest Common Factor Method

Greatest Common Factor of 217,1667 By Matching Biggest Common Factor Method

Now, list down the factors of 217

:

1,7,31,217

Now, list down the factors of 1667

:

1,1667

Greatest Common Factor

We found the factors 217,1667 . The biggest common factor number is the GCF number.
So the greatest common factor 217,1667 is 1.

Lets's calculate LCM of 364,412

Lowest Common Multiple of 364,412 using Common Division

2 364, 412
2 182, 206
91, 103

∴ So the LCM of the given numbers is 2 x 2 x 91 x 103 = 37492

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37492

Therefore, the GCF of Fractions 217/364,1667/412 is 1/37492

Least Common Multiple of 364,412 with GCF Formula

Least Common Multiple of 364,412 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 364,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(364,412) = 4

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

GCF(364,412) x common factors =4 x 1 = 4

LCM(364,412) = ( 364 × 412 ) / 4

LCM(364,412) = 149968 / 4

LCM(364,412) = 37492


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FAQs on GCF of Fractions of 217/364, 1667/412

1. What is the HCF of 217,1667?

The HCF of 217,1667 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 217/364, 1667/412?

Answer: GCF of Numerators as per given numbers 217/364, 1667/412 is

GCF of Numerators i.e. for 217,1667 is 1

LCM of denominators i.e. for 364,412 is 37492.

Thus, GCF of Fractions is 1/37492.Finally, GCF of Fractions for 217/364, 1667/412 is 1/37492.