How to Find GCF of 836/473, 1564/814?

GCF of 836/473, 1564/814

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 836/473, 1564/814 i.e 4/35002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 836/473, 1564/814.

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 836/473,1564/814?

Given fractions are 836/473,1564/814

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 836/473,1564/814, numerators are 836,1564

Denominators are 473,814

The GCF of 836,1564 is 4 .

LCM of 473,814 is 35002.

The greatest common factor of 836/473,1564/814 = [GCF of 836,1564]/[LCM of 473,814]= 4/35002

Therefore, the GCF of 836/473,1564/814 is 4/35002.

Greatest Common Factor of 836,1564

To find the highest common factor of 836,1564, we have to find the factors of both numbers and list the highest common factor.

The factors of 836 are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836

The factors of 1564 are 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564

The HCF of 836,1564 is 4.

Lets's calculate GCF of 836,1564

Greatest Common Factor (GCF) of 836,1564 By Common Division

2	836, 1564
2	418, 782
	209, 391

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 836,1564 By Matching Biggest Common Factor Method

Now, list down the factors of 836

1,2,4,11,19,22,38,44,76,209,418,836

Now, list down the factors of 1564

1,2,4,17,23,34,46,68,92,391,782,1564

Greatest Common Factor

We found the factors 836,1564 . The biggest common factor number is the GCF number.
So the greatest common factor 836,1564 is 4.

Lets's calculate LCM of 473,814

Lowest Common Multiple of 473,814 using Common Division

11	473, 814
	43, 74

∴ So the LCM of the given numbers is 11 x 43 x 74 = 35002

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/35002

Therefore, the GCF of Fractions 836/473,1564/814 is 4/35002

Least Common Multiple of 473,814 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 473,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(473,814) = 11

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

GCF(473,814) x common factors =11 x 1 = 11

LCM(473,814) = ( 473 × 814 ) / 11

LCM(473,814) = 385022 / 11

LCM(473,814) = 35002

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FAQs on GCF of Fractions of 836/473, 1564/814

1. What is the HCF of 836,1564?

The HCF of 836,1564 is 4

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 836/473, 1564/814?

Answer: GCF of Numerators as per given numbers 836/473, 1564/814 is

GCF of Numerators i.e. for 836,1564 is 4

LCM of denominators i.e. for 473,814 is 35002.

Thus, GCF of Fractions is 4/35002.Finally, GCF of Fractions for 836/473, 1564/814 is 4/35002.