How to Find GCF of 770/472, 414/820?

GCF of 770/472, 414/820

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 770/472, 414/820 i.e 2/96760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/472, 414/820.

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 770/472,414/820?

Given fractions are 770/472,414/820

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 770/472,414/820, numerators are 770,414

Denominators are 472,820

The GCF of 770,414 is 2 .

LCM of 472,820 is 96760.

The greatest common factor of 770/472,414/820 = [GCF of 770,414]/[LCM of 472,820]= 2/96760

Therefore, the GCF of 770/472,414/820 is 2/96760.

Greatest Common Factor of 770,414

To find the highest common factor of 770,414, 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 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 770,414 is 2.

Lets's calculate GCF of 770,414

Greatest Common Factor (GCF) of 770,414 By Common Division

2	770, 414
	385, 207

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

Greatest Common Factor of 770,414 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 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 770,414 . The biggest common factor number is the GCF number.
So the greatest common factor 770,414 is 2.

Lets's calculate LCM of 472,820

Lowest Common Multiple of 472,820 using Common Division

2	472, 820
2	236, 410
	118, 205

∴ So the LCM of the given numbers is 2 x 2 x 118 x 205 = 96760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/96760

Therefore, the GCF of Fractions 770/472,414/820 is 2/96760

Least Common Multiple of 472,820 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 472,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(472,820) = 4

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

GCF(472,820) x common factors =4 x 1 = 4

LCM(472,820) = ( 472 × 820 ) / 4

LCM(472,820) = 387040 / 4

LCM(472,820) = 96760

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FAQs on GCF of Fractions of 770/472, 414/820

1. What is the HCF of 770,414?

The HCF of 770,414 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 770/472, 414/820?

Answer: GCF of Numerators as per given numbers 770/472, 414/820 is

GCF of Numerators i.e. for 770,414 is 2

LCM of denominators i.e. for 472,820 is 96760.

Thus, GCF of Fractions is 2/96760.Finally, GCF of Fractions for 770/472, 414/820 is 2/96760.