How to Find GCF of 86/702, 14/185, 308/564?

GCF of 86/702, 14/185, 308/564

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 86/702, 14/185, 308/564 i.e 2/12207780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/702, 14/185, 308/564.

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 86/702,14/185,308/564?

Given fractions are 86/702,14/185,308/564

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 86/702,14/185,308/564, numerators are 86,14,308

Denominators are 702,185,564

The GCF of 86,14,308 is 2 .

LCM of 702,185,564 is 12207780.

The greatest common factor of 86/702,14/185,308/564 = [GCF of 86,14,308]/[LCM of 702,185,564]= 2/12207780

Therefore, the GCF of 86/702,14/185,308/564 is 2/12207780.

Greatest Common Factor of 86,14,308

To find the highest common factor of 86,14,308, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 14 are 1, 2, 7, 14

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The HCF of 86,14,308 is 2.

Lets's calculate GCF of 86,14,308

Greatest Common Factor (GCF) of 86,14,308 By Common Division

2	86, 14, 308
	43, 7, 154

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

Greatest Common Factor of 86,14,308 By Matching Biggest Common Factor Method

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 308

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors 86,14,308 . The biggest common factor number is the GCF number.
So the greatest common factor 86,14,308 is 2.

Lets's calculate LCM of 702,185,564

Lowest Common Multiple of 702,185,564 using Common Division

2	702, 185, 564
3	351, 185, 282
	117, 185, 94

∴ So the LCM of the given numbers is 2 x 3 x 117 x 185 x 94 = 12207780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12207780

Therefore, the GCF of Fractions 86/702,14/185,308/564 is 2/12207780

Least Common Multiple of 702,185,564 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 702,185,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(702,185,564) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(702,185,564) x common factors =1 x 6 = 6

LCM(702,185,564) = ( 702 × 185 × 564 ) / 6

LCM(702,185,564) = 73246680 / 6

LCM(702,185,564) = 12207780

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 86/702, 14/185, 308/564

1. What is the HCF of 86,14,308?

The HCF of 86,14,308 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 86/702, 14/185, 308/564?

Answer: GCF of Numerators as per given numbers 86/702, 14/185, 308/564 is

GCF of Numerators i.e. for 86,14,308 is 2

LCM of denominators i.e. for 702,185,564 is 12207780.

Thus, GCF of Fractions is 2/12207780.Finally, GCF of Fractions for 86/702, 14/185, 308/564 is 2/12207780.