How to Find GCF of 715/701, 1749/2600?

GCF of 715/701, 1749/2600

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 715/701, 1749/2600 i.e 11/1822600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 715/701, 1749/2600.

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 715/701,1749/2600?

Given fractions are 715/701,1749/2600

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 715/701,1749/2600, numerators are 715,1749

Denominators are 701,2600

The GCF of 715,1749 is 11 .

LCM of 701,2600 is 1822600.

The greatest common factor of 715/701,1749/2600 = [GCF of 715,1749]/[LCM of 701,2600]= 11/1822600

Therefore, the GCF of 715/701,1749/2600 is 11/1822600.

Greatest Common Factor of 715,1749

To find the highest common factor of 715,1749, we have to find the factors of both numbers and list the highest common factor.

The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715

The factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749

The HCF of 715,1749 is 11.

Lets's calculate GCF of 715,1749

Greatest Common Factor (GCF) of 715,1749 By Common Division

11	715, 1749
	65, 159

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 715,1749 By Matching Biggest Common Factor Method

Now, list down the factors of 715

1,5,11,13,55,65,143,715

Now, list down the factors of 1749

1,3,11,33,53,159,583,1749

Greatest Common Factor

We found the factors 715,1749 . The biggest common factor number is the GCF number.
So the greatest common factor 715,1749 is 11.

Lets's calculate LCM of 701,2600

Lowest Common Multiple of 701,2600 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1822600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/1822600

Therefore, the GCF of Fractions 715/701,1749/2600 is 11/1822600

Least Common Multiple of 701,2600 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 701,2600 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(701,2600) = 1

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

GCF(701,2600) x common factors =1 x 1 = 1

LCM(701,2600) = ( 701 × 2600 ) / 1

LCM(701,2600) = 1822600 / 1

LCM(701,2600) = 1822600

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FAQs on GCF of Fractions of 715/701, 1749/2600

1. What is the HCF of 715,1749?

The HCF of 715,1749 is 11

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 715/701, 1749/2600?

Answer: GCF of Numerators as per given numbers 715/701, 1749/2600 is

GCF of Numerators i.e. for 715,1749 is 11

LCM of denominators i.e. for 701,2600 is 1822600.

Thus, GCF of Fractions is 11/1822600.Finally, GCF of Fractions for 715/701, 1749/2600 is 11/1822600.