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GCF of 172/214, 723/262

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 172/214, 723/262 i.e 1/28034 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/214, 723/262.

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 172/214,723/262?

Given fractions are 172/214,723/262

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 172/214,723/262, numerators are 172,723

Denominators are 214,262

The GCF of 172,723 is 1 .

LCM of 214,262 is 28034.

The greatest common factor of 172/214,723/262 = [GCF of 172,723]/[LCM of 214,262]= 1/28034

Therefore, the GCF of 172/214,723/262 is 1/28034.

Greatest Common Factor of 172,723

To find the highest common factor of 172,723, we have to find the factors of both numbers and list the highest common factor.

The factors of 172 are 1, 2, 4, 43, 86, 172

The factors of 723 are 1, 3, 241, 723

The HCF of 172,723 is 1.

Lets's calculate GCF of 172,723

Greatest Common Factor (GCF) of 172,723 By Common Division

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

Greatest Common Factor of 172,723 By Matching Biggest Common Factor Method

Greatest Common Factor of 172,723 By Matching Biggest Common Factor Method

Now, list down the factors of 172

:

1,2,4,43,86,172

Now, list down the factors of 723

:

1,3,241,723

Greatest Common Factor

We found the factors 172,723 . The biggest common factor number is the GCF number.
So the greatest common factor 172,723 is 1.

Lets's calculate LCM of 214,262

Lowest Common Multiple of 214,262 using Common Division

2 214, 262
107, 131

∴ So the LCM of the given numbers is 2 x 107 x 131 = 28034

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28034

Therefore, the GCF of Fractions 172/214,723/262 is 1/28034

Least Common Multiple of 214,262 with GCF Formula

Least Common Multiple of 214,262 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 214,262 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,262) = 2

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

GCF(214,262) x common factors =2 x 1 = 2

LCM(214,262) = ( 214 × 262 ) / 2

LCM(214,262) = 56068 / 2

LCM(214,262) = 28034


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FAQs on GCF of Fractions of 172/214, 723/262

1. What is the HCF of 172,723?

The HCF of 172,723 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 172/214, 723/262?

Answer: GCF of Numerators as per given numbers 172/214, 723/262 is

GCF of Numerators i.e. for 172,723 is 1

LCM of denominators i.e. for 214,262 is 28034.

Thus, GCF of Fractions is 1/28034.Finally, GCF of Fractions for 172/214, 723/262 is 1/28034.