How to Find GCF of 7814/262, 8488/1075?

GCF of 7814/262, 8488/1075

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 7814/262, 8488/1075 i.e 2/281650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7814/262, 8488/1075.

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 7814/262,8488/1075?

Given fractions are 7814/262,8488/1075

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 7814/262,8488/1075, numerators are 7814,8488

Denominators are 262,1075

The GCF of 7814,8488 is 2 .

LCM of 262,1075 is 281650.

The greatest common factor of 7814/262,8488/1075 = [GCF of 7814,8488]/[LCM of 262,1075]= 2/281650

Therefore, the GCF of 7814/262,8488/1075 is 2/281650.

Greatest Common Factor of 7814,8488

To find the highest common factor of 7814,8488, we have to find the factors of both numbers and list the highest common factor.

The factors of 7814 are 1, 2, 3907, 7814

The factors of 8488 are 1, 2, 4, 8, 1061, 2122, 4244, 8488

The HCF of 7814,8488 is 2.

Lets's calculate GCF of 7814,8488

Greatest Common Factor (GCF) of 7814,8488 By Common Division

2	7814, 8488
	3907, 4244

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

Greatest Common Factor of 7814,8488 By Matching Biggest Common Factor Method

Now, list down the factors of 7814

1,2,3907,7814

Now, list down the factors of 8488

1,2,4,8,1061,2122,4244,8488

Greatest Common Factor

We found the factors 7814,8488 . The biggest common factor number is the GCF number.
So the greatest common factor 7814,8488 is 2.

Lets's calculate LCM of 262,1075

Lowest Common Multiple of 262,1075 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 281650

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/281650

Therefore, the GCF of Fractions 7814/262,8488/1075 is 2/281650

Least Common Multiple of 262,1075 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 262,1075 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(262,1075) = 1

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

GCF(262,1075) x common factors =1 x 1 = 1

LCM(262,1075) = ( 262 × 1075 ) / 1

LCM(262,1075) = 281650 / 1

LCM(262,1075) = 281650

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FAQs on GCF of Fractions of 7814/262, 8488/1075

1. What is the HCF of 7814,8488?

The HCF of 7814,8488 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 7814/262, 8488/1075?

Answer: GCF of Numerators as per given numbers 7814/262, 8488/1075 is

GCF of Numerators i.e. for 7814,8488 is 2

LCM of denominators i.e. for 262,1075 is 281650.

Thus, GCF of Fractions is 2/281650.Finally, GCF of Fractions for 7814/262, 8488/1075 is 2/281650.