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GCF of 705/85, 974/1684

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 705/85, 974/1684 i.e 1/143140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/85, 974/1684.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 705/85,974/1684?

Given fractions are 705/85,974/1684

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 705/85,974/1684, numerators are 705,974

Denominators are 85,1684

The GCF of 705,974 is 1 .

LCM of 85,1684 is 143140.

The greatest common factor of 705/85,974/1684 = [GCF of 705,974]/[LCM of 85,1684]= 1/143140

Therefore, the GCF of 705/85,974/1684 is 1/143140.

Greatest Common Factor of 705,974

To find the highest common factor of 705,974, we have to find the factors of both numbers and list the highest common factor.

The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705

The factors of 974 are 1, 2, 487, 974

The HCF of 705,974 is 1.

Lets's calculate GCF of 705,974

Greatest Common Factor (GCF) of 705,974 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 705,974 By Matching Biggest Common Factor Method

Greatest Common Factor of 705,974 By Matching Biggest Common Factor Method

Now, list down the factors of 705

:

1,3,5,15,47,141,235,705

Now, list down the factors of 974

:

1,2,487,974

Greatest Common Factor

We found the factors 705,974 . The biggest common factor number is the GCF number.
So the greatest common factor 705,974 is 1.

Lets's calculate LCM of 85,1684

Lowest Common Multiple of 85,1684 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 143140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/143140

Therefore, the GCF of Fractions 705/85,974/1684 is 1/143140

Least Common Multiple of 85,1684 with GCF Formula

Least Common Multiple of 85,1684 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 85,1684 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(85,1684) = 1

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

GCF(85,1684) x common factors =1 x 1 = 1

LCM(85,1684) = ( 85 × 1684 ) / 1

LCM(85,1684) = 143140 / 1

LCM(85,1684) = 143140


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 705/85, 974/1684

1. What is the HCF of 705,974?

The HCF of 705,974 is 1

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 705/85, 974/1684?

Answer: GCF of Numerators as per given numbers 705/85, 974/1684 is

GCF of Numerators i.e. for 705,974 is 1

LCM of denominators i.e. for 85,1684 is 143140.

Thus, GCF of Fractions is 1/143140.Finally, GCF of Fractions for 705/85, 974/1684 is 1/143140.