How to Find GCF of 770/692, 500/141?

GCF of 770/692, 500/141

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 770/692, 500/141 i.e 10/97572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/692, 500/141.

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 770/692,500/141?

Given fractions are 770/692,500/141

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 770/692,500/141, numerators are 770,500

Denominators are 692,141

The GCF of 770,500 is 10 .

LCM of 692,141 is 97572.

The greatest common factor of 770/692,500/141 = [GCF of 770,500]/[LCM of 692,141]= 10/97572

Therefore, the GCF of 770/692,500/141 is 10/97572.

Greatest Common Factor of 770,500

To find the highest common factor of 770,500, we have to find the factors of both numbers and list the highest common factor.

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The HCF of 770,500 is 10.

Lets's calculate GCF of 770,500

Greatest Common Factor (GCF) of 770,500 By Common Division

2	770, 500
5	385, 250
	77, 50

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 770,500 By Matching Biggest Common Factor Method

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Now, list down the factors of 500

1,2,4,5,10,20,25,50,100,125,250,500

Greatest Common Factor

We found the factors 770,500 . The biggest common factor number is the GCF number.
So the greatest common factor 770,500 is 10.

Lets's calculate LCM of 692,141

Lowest Common Multiple of 692,141 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 97572

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/97572

Therefore, the GCF of Fractions 770/692,500/141 is 10/97572

Least Common Multiple of 692,141 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 692,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(692,141) = 1

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

GCF(692,141) x common factors =1 x 1 = 1

LCM(692,141) = ( 692 × 141 ) / 1

LCM(692,141) = 97572 / 1

LCM(692,141) = 97572

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FAQs on GCF of Fractions of 770/692, 500/141

1. What is the HCF of 770,500?

The HCF of 770,500 is 10

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 770/692, 500/141?

Answer: GCF of Numerators as per given numbers 770/692, 500/141 is

GCF of Numerators i.e. for 770,500 is 10

LCM of denominators i.e. for 692,141 is 97572.

Thus, GCF of Fractions is 10/97572.Finally, GCF of Fractions for 770/692, 500/141 is 10/97572.