How to Find GCF of 770/575, 2218/689?

GCF of 770/575, 2218/689

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 770/575, 2218/689 i.e 2/396175 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/575, 2218/689.

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 770/575,2218/689?

Given fractions are 770/575,2218/689

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 770/575,2218/689, numerators are 770,2218

Denominators are 575,689

The GCF of 770,2218 is 2 .

LCM of 575,689 is 396175.

The greatest common factor of 770/575,2218/689 = [GCF of 770,2218]/[LCM of 575,689]= 2/396175

Therefore, the GCF of 770/575,2218/689 is 2/396175.

Greatest Common Factor of 770,2218

To find the highest common factor of 770,2218, 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 2218 are 1, 2, 1109, 2218

The HCF of 770,2218 is 2.

Lets's calculate GCF of 770,2218

Greatest Common Factor (GCF) of 770,2218 By Common Division

2	770, 2218
	385, 1109

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

Greatest Common Factor of 770,2218 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 2218

1,2,1109,2218

Greatest Common Factor

We found the factors 770,2218 . The biggest common factor number is the GCF number.
So the greatest common factor 770,2218 is 2.

Lets's calculate LCM of 575,689

Lowest Common Multiple of 575,689 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 396175

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/396175

Therefore, the GCF of Fractions 770/575,2218/689 is 2/396175

Least Common Multiple of 575,689 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 575,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(575,689) = 1

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

GCF(575,689) x common factors =1 x 1 = 1

LCM(575,689) = ( 575 × 689 ) / 1

LCM(575,689) = 396175 / 1

LCM(575,689) = 396175

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FAQs on GCF of Fractions of 770/575, 2218/689

1. What is the HCF of 770,2218?

The HCF of 770,2218 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 770/575, 2218/689?

Answer: GCF of Numerators as per given numbers 770/575, 2218/689 is

GCF of Numerators i.e. for 770,2218 is 2

LCM of denominators i.e. for 575,689 is 396175.

Thus, GCF of Fractions is 2/396175.Finally, GCF of Fractions for 770/575, 2218/689 is 2/396175.