How to Find GCF of 1564/275, 7930/257?

GCF of 1564/275, 7930/257

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 1564/275, 7930/257 i.e 2/70675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1564/275, 7930/257.

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 1564/275,7930/257?

Given fractions are 1564/275,7930/257

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 1564/275,7930/257, numerators are 1564,7930

Denominators are 275,257

The GCF of 1564,7930 is 2 .

LCM of 275,257 is 70675.

The greatest common factor of 1564/275,7930/257 = [GCF of 1564,7930]/[LCM of 275,257]= 2/70675

Therefore, the GCF of 1564/275,7930/257 is 2/70675.

Greatest Common Factor of 1564,7930

To find the highest common factor of 1564,7930, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 7930 are 1, 2, 5, 10, 13, 26, 61, 65, 122, 130, 305, 610, 793, 1586, 3965, 7930

The HCF of 1564,7930 is 2.

Lets's calculate GCF of 1564,7930

Greatest Common Factor (GCF) of 1564,7930 By Common Division

2	1564, 7930
	782, 3965

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

Greatest Common Factor of 1564,7930 By Matching Biggest Common Factor Method

Now, list down the factors of 1564

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

Now, list down the factors of 7930

1,2,5,10,13,26,61,65,122,130,305,610,793,1586,3965,7930

Greatest Common Factor

We found the factors 1564,7930 . The biggest common factor number is the GCF number.
So the greatest common factor 1564,7930 is 2.

Lets's calculate LCM of 275,257

Lowest Common Multiple of 275,257 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 70675

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/70675

Therefore, the GCF of Fractions 1564/275,7930/257 is 2/70675

Least Common Multiple of 275,257 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 275,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(275,257) = 1

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

GCF(275,257) x common factors =1 x 1 = 1

LCM(275,257) = ( 275 × 257 ) / 1

LCM(275,257) = 70675 / 1

LCM(275,257) = 70675

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FAQs on GCF of Fractions of 1564/275, 7930/257

1. What is the HCF of 1564,7930?

The HCF of 1564,7930 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 1564/275, 7930/257?

Answer: GCF of Numerators as per given numbers 1564/275, 7930/257 is

GCF of Numerators i.e. for 1564,7930 is 2

LCM of denominators i.e. for 275,257 is 70675.

Thus, GCF of Fractions is 2/70675.Finally, GCF of Fractions for 1564/275, 7930/257 is 2/70675.