How to Find GCF of 705/10, 728/357?

GCF of 705/10, 728/357

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 705/10, 728/357 i.e 1/3570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/10, 728/357.

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 705/10,728/357?

Given fractions are 705/10,728/357

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 705/10,728/357, numerators are 705,728

Denominators are 10,357

The GCF of 705,728 is 1 .

LCM of 10,357 is 3570.

The greatest common factor of 705/10,728/357 = [GCF of 705,728]/[LCM of 10,357]= 1/3570

Therefore, the GCF of 705/10,728/357 is 1/3570.

Greatest Common Factor of 705,728

To find the highest common factor of 705,728, 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 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The HCF of 705,728 is 1.

Lets's calculate GCF of 705,728

Greatest Common Factor (GCF) of 705,728 By Common Division

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

Greatest Common Factor of 705,728 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 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Greatest Common Factor

We found the factors 705,728 . The biggest common factor number is the GCF number.
So the greatest common factor 705,728 is 1.

Lets's calculate LCM of 10,357

Lowest Common Multiple of 10,357 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3570

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3570

Therefore, the GCF of Fractions 705/10,728/357 is 1/3570

Least Common Multiple of 10,357 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 10,357 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(10,357) = 1

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

GCF(10,357) x common factors =1 x 1 = 1

LCM(10,357) = ( 10 × 357 ) / 1

LCM(10,357) = 3570 / 1

LCM(10,357) = 3570

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FAQs on GCF of Fractions of 705/10, 728/357

1. What is the HCF of 705,728?

The HCF of 705,728 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 705/10, 728/357?

Answer: GCF of Numerators as per given numbers 705/10, 728/357 is

GCF of Numerators i.e. for 705,728 is 1

LCM of denominators i.e. for 10,357 is 3570.

Thus, GCF of Fractions is 1/3570.Finally, GCF of Fractions for 705/10, 728/357 is 1/3570.