How to Find GCF of 629/21, 690/142?

GCF of 629/21, 690/142

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 629/21, 690/142 i.e 1/2982 easily. The following is the detailed procedure to determine the greatest common factor of fractions 629/21, 690/142.

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 629/21,690/142?

Given fractions are 629/21,690/142

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 629/21,690/142, numerators are 629,690

Denominators are 21,142

The GCF of 629,690 is 1 .

LCM of 21,142 is 2982.

The greatest common factor of 629/21,690/142 = [GCF of 629,690]/[LCM of 21,142]= 1/2982

Therefore, the GCF of 629/21,690/142 is 1/2982.

Greatest Common Factor of 629,690

To find the highest common factor of 629,690, we have to find the factors of both numbers and list the highest common factor.

The factors of 629 are 1, 17, 37, 629

The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

The HCF of 629,690 is 1.

Lets's calculate GCF of 629,690

Greatest Common Factor (GCF) of 629,690 By Common Division

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

Greatest Common Factor of 629,690 By Matching Biggest Common Factor Method

Now, list down the factors of 629

1,17,37,629

Now, list down the factors of 690

1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690

Greatest Common Factor

We found the factors 629,690 . The biggest common factor number is the GCF number.
So the greatest common factor 629,690 is 1.

Lets's calculate LCM of 21,142

Lowest Common Multiple of 21,142 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2982

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2982

Therefore, the GCF of Fractions 629/21,690/142 is 1/2982

Least Common Multiple of 21,142 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 21,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,142) = 1

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

GCF(21,142) x common factors =1 x 1 = 1

LCM(21,142) = ( 21 × 142 ) / 1

LCM(21,142) = 2982 / 1

LCM(21,142) = 2982

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FAQs on GCF of Fractions of 629/21, 690/142

1. What is the HCF of 629,690?

The HCF of 629,690 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 629/21, 690/142?

Answer: GCF of Numerators as per given numbers 629/21, 690/142 is

GCF of Numerators i.e. for 629,690 is 1

LCM of denominators i.e. for 21,142 is 2982.

Thus, GCF of Fractions is 1/2982.Finally, GCF of Fractions for 629/21, 690/142 is 1/2982.