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GCF of 702/65, 189/142

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 702/65, 189/142 i.e 27/9230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/65, 189/142.

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 702/65,189/142?

Given fractions are 702/65,189/142

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 702/65,189/142, numerators are 702,189

Denominators are 65,142

The GCF of 702,189 is 27 .

LCM of 65,142 is 9230.

The greatest common factor of 702/65,189/142 = [GCF of 702,189]/[LCM of 65,142]= 27/9230

Therefore, the GCF of 702/65,189/142 is 27/9230.

Greatest Common Factor of 702,189

To find the highest common factor of 702,189, we have to find the factors of both numbers and list the highest common factor.

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The HCF of 702,189 is 27.

Lets's calculate GCF of 702,189

Greatest Common Factor (GCF) of 702,189 By Common Division

3 702, 189
3 234, 63
3 78, 21
26, 7

∴ So the GCF of the given numbers is 3 x 3 x 3 = 27

Greatest Common Factor of 702,189 By Matching Biggest Common Factor Method

Greatest Common Factor of 702,189 By Matching Biggest Common Factor Method

Now, list down the factors of 702

:

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Now, list down the factors of 189

:

1,3,7,9,21,27,63,189

Greatest Common Factor

We found the factors 702,189 . The biggest common factor number is the GCF number.
So the greatest common factor 702,189 is 27.

Lets's calculate LCM of 65,142

Lowest Common Multiple of 65,142 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9230

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/9230

Therefore, the GCF of Fractions 702/65,189/142 is 27/9230

Least Common Multiple of 65,142 with GCF Formula

Least Common Multiple of 65,142 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 65,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,142) = 1

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

GCF(65,142) x common factors =1 x 1 = 1

LCM(65,142) = ( 65 × 142 ) / 1

LCM(65,142) = 9230 / 1

LCM(65,142) = 9230


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FAQs on GCF of Fractions of 702/65, 189/142

1. What is the HCF of 702,189?

The HCF of 702,189 is 27

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 702/65, 189/142?

Answer: GCF of Numerators as per given numbers 702/65, 189/142 is

GCF of Numerators i.e. for 702,189 is 27

LCM of denominators i.e. for 65,142 is 9230.

Thus, GCF of Fractions is 27/9230.Finally, GCF of Fractions for 702/65, 189/142 is 27/9230.