How to Find GCF of 78/31, 67/53, 289/74?

GCF of 78/31, 67/53, 289/74

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 78/31, 67/53, 289/74 i.e 1/121582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/31, 67/53, 289/74.

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 78/31,67/53,289/74?

Given fractions are 78/31,67/53,289/74

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 78/31,67/53,289/74, numerators are 78,67,289

Denominators are 31,53,74

The GCF of 78,67,289 is 1 .

LCM of 31,53,74 is 121582.

The greatest common factor of 78/31,67/53,289/74 = [GCF of 78,67,289]/[LCM of 31,53,74]= 1/121582

Therefore, the GCF of 78/31,67/53,289/74 is 1/121582.

Greatest Common Factor of 78,67,289

To find the highest common factor of 78,67,289, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 67 are 1, 67

The factors of 289 are 1, 17, 289

The HCF of 78,67,289 is 1.

Lets's calculate GCF of 78,67,289

Greatest Common Factor (GCF) of 78,67,289 By Common Division

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

Greatest Common Factor of 78,67,289 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 67

1,67

Now, list down the factors of 289

1,17,289

Greatest Common Factor

We found the factors 78,67,289 . The biggest common factor number is the GCF number.
So the greatest common factor 78,67,289 is 1.

Lets's calculate LCM of 31,53,74

Lowest Common Multiple of 31,53,74 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 121582

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/121582

Therefore, the GCF of Fractions 78/31,67/53,289/74 is 1/121582

Least Common Multiple of 31,53,74 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 31,53,74 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,53,74) = 1

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

GCF(31,53,74) x common factors =1 x 1 = 1

LCM(31,53,74) = ( 31 × 53 × 74 ) / 1

LCM(31,53,74) = 121582 / 1

LCM(31,53,74) = 121582

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FAQs on GCF of Fractions of 78/31, 67/53, 289/74

1. What is the HCF of 78,67,289?

The HCF of 78,67,289 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 78/31, 67/53, 289/74?

Answer: GCF of Numerators as per given numbers 78/31, 67/53, 289/74 is

GCF of Numerators i.e. for 78,67,289 is 1

LCM of denominators i.e. for 31,53,74 is 121582.

Thus, GCF of Fractions is 1/121582.Finally, GCF of Fractions for 78/31, 67/53, 289/74 is 1/121582.