How to Find GCF of 5978/157, 5606/1465?

GCF of 5978/157, 5606/1465

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 5978/157, 5606/1465 i.e 2/230005 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5978/157, 5606/1465.

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 5978/157,5606/1465?

Given fractions are 5978/157,5606/1465

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 5978/157,5606/1465, numerators are 5978,5606

Denominators are 157,1465

The GCF of 5978,5606 is 2 .

LCM of 157,1465 is 230005.

The greatest common factor of 5978/157,5606/1465 = [GCF of 5978,5606]/[LCM of 157,1465]= 2/230005

Therefore, the GCF of 5978/157,5606/1465 is 2/230005.

Greatest Common Factor of 5978,5606

To find the highest common factor of 5978,5606, we have to find the factors of both numbers and list the highest common factor.

The factors of 5978 are 1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978

The factors of 5606 are 1, 2, 2803, 5606

The HCF of 5978,5606 is 2.

Lets's calculate GCF of 5978,5606

Greatest Common Factor (GCF) of 5978,5606 By Common Division

2	5978, 5606
	2989, 2803

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

Greatest Common Factor of 5978,5606 By Matching Biggest Common Factor Method

Now, list down the factors of 5978

1,2,7,14,49,61,98,122,427,854,2989,5978

Now, list down the factors of 5606

1,2,2803,5606

Greatest Common Factor

We found the factors 5978,5606 . The biggest common factor number is the GCF number.
So the greatest common factor 5978,5606 is 2.

Lets's calculate LCM of 157,1465

Lowest Common Multiple of 157,1465 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 230005

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/230005

Therefore, the GCF of Fractions 5978/157,5606/1465 is 2/230005

Least Common Multiple of 157,1465 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 157,1465 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(157,1465) = 1

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

GCF(157,1465) x common factors =1 x 1 = 1

LCM(157,1465) = ( 157 × 1465 ) / 1

LCM(157,1465) = 230005 / 1

LCM(157,1465) = 230005

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 5978/157, 5606/1465

1. What is the HCF of 5978,5606?

The HCF of 5978,5606 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 5978/157, 5606/1465?

Answer: GCF of Numerators as per given numbers 5978/157, 5606/1465 is

GCF of Numerators i.e. for 5978,5606 is 2

LCM of denominators i.e. for 157,1465 is 230005.

Thus, GCF of Fractions is 2/230005.Finally, GCF of Fractions for 5978/157, 5606/1465 is 2/230005.