How to Find GCF of 85/74, 61/89, 606/409?

GCF of 85/74, 61/89, 606/409

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 85/74, 61/89, 606/409 i.e 1/2693674 easily. The following is the detailed procedure to determine the greatest common factor of fractions 85/74, 61/89, 606/409.

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 85/74,61/89,606/409?

Given fractions are 85/74,61/89,606/409

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 85/74,61/89,606/409, numerators are 85,61,606

Denominators are 74,89,409

The GCF of 85,61,606 is 1 .

LCM of 74,89,409 is 2693674.

The greatest common factor of 85/74,61/89,606/409 = [GCF of 85,61,606]/[LCM of 74,89,409]= 1/2693674

Therefore, the GCF of 85/74,61/89,606/409 is 1/2693674.

Greatest Common Factor of 85,61,606

To find the highest common factor of 85,61,606, we have to find the factors of both numbers and list the highest common factor.

The factors of 85 are 1, 5, 17, 85

The factors of 61 are 1, 61

The factors of 606 are 1, 2, 3, 6, 101, 202, 303, 606

The HCF of 85,61,606 is 1.

Lets's calculate GCF of 85,61,606

Greatest Common Factor (GCF) of 85,61,606 By Common Division

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

Greatest Common Factor of 85,61,606 By Matching Biggest Common Factor Method

Now, list down the factors of 85

1,5,17,85

Now, list down the factors of 61

1,61

Now, list down the factors of 606

1,2,3,6,101,202,303,606

Greatest Common Factor

We found the factors 85,61,606 . The biggest common factor number is the GCF number.
So the greatest common factor 85,61,606 is 1.

Lets's calculate LCM of 74,89,409

Lowest Common Multiple of 74,89,409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2693674

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2693674

Therefore, the GCF of Fractions 85/74,61/89,606/409 is 1/2693674

Least Common Multiple of 74,89,409 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 74,89,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,89,409) = 1

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

GCF(74,89,409) x common factors =1 x 1 = 1

LCM(74,89,409) = ( 74 × 89 × 409 ) / 1

LCM(74,89,409) = 2693674 / 1

LCM(74,89,409) = 2693674

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FAQs on GCF of Fractions of 85/74, 61/89, 606/409

1. What is the HCF of 85,61,606?

The HCF of 85,61,606 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 85/74, 61/89, 606/409?

Answer: GCF of Numerators as per given numbers 85/74, 61/89, 606/409 is

GCF of Numerators i.e. for 85,61,606 is 1

LCM of denominators i.e. for 74,89,409 is 2693674.

Thus, GCF of Fractions is 1/2693674.Finally, GCF of Fractions for 85/74, 61/89, 606/409 is 1/2693674.