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GCF of 562/36, 214/172

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 562/36, 214/172 i.e 2/1548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 562/36, 214/172.

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 562/36,214/172?

Given fractions are 562/36,214/172

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 562/36,214/172, numerators are 562,214

Denominators are 36,172

The GCF of 562,214 is 2 .

LCM of 36,172 is 1548.

The greatest common factor of 562/36,214/172 = [GCF of 562,214]/[LCM of 36,172]= 2/1548

Therefore, the GCF of 562/36,214/172 is 2/1548.

Greatest Common Factor of 562,214

To find the highest common factor of 562,214, we have to find the factors of both numbers and list the highest common factor.

The factors of 562 are 1, 2, 281, 562

The factors of 214 are 1, 2, 107, 214

The HCF of 562,214 is 2.

Lets's calculate GCF of 562,214

Greatest Common Factor (GCF) of 562,214 By Common Division

2 562, 214
281, 107

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

Greatest Common Factor of 562,214 By Matching Biggest Common Factor Method

Greatest Common Factor of 562,214 By Matching Biggest Common Factor Method

Now, list down the factors of 562

:

1,2,281,562

Now, list down the factors of 214

:

1,2,107,214

Greatest Common Factor

We found the factors 562,214 . The biggest common factor number is the GCF number.
So the greatest common factor 562,214 is 2.

Lets's calculate LCM of 36,172

Lowest Common Multiple of 36,172 using Common Division

2 36, 172
2 18, 86
9, 43

∴ So the LCM of the given numbers is 2 x 2 x 9 x 43 = 1548

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1548

Therefore, the GCF of Fractions 562/36,214/172 is 2/1548

Least Common Multiple of 36,172 with GCF Formula

Least Common Multiple of 36,172 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 36,172 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,172) = 4

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

GCF(36,172) x common factors =4 x 1 = 4

LCM(36,172) = ( 36 × 172 ) / 4

LCM(36,172) = 6192 / 4

LCM(36,172) = 1548


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FAQs on GCF of Fractions of 562/36, 214/172

1. What is the HCF of 562,214?

The HCF of 562,214 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 562/36, 214/172?

Answer: GCF of Numerators as per given numbers 562/36, 214/172 is

GCF of Numerators i.e. for 562,214 is 2

LCM of denominators i.e. for 36,172 is 1548.

Thus, GCF of Fractions is 2/1548.Finally, GCF of Fractions for 562/36, 214/172 is 2/1548.