Greatest Common Factor of 67/14, 72/10, 300/77

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 67/14, 72/10, 300/77

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 67/14,72/10,300/77

Given fractions are 67/14,72/10,300/77

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 67,72,300

Greatest Common Factor of Numerators i.e. GCF of 67,72,300 is 1 .

LCM of Denominators means LCM of 14,10,77 as per the given fractions.

LCM of 14,10,77 is 770 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 67,72,300

GCF of Fractions 67/14,72/10,300/77 is 1/770

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

Greatest Common Factor of 67,72,300 By Matching Biggest Common Factor Method

Greatest Common Factor of 67,72,300 By Matching Biggest Common Factor Method

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 67,72,300 . The biggest common factor number is the GCF number.
So the greatest common factor 67,72,300 is 1.

Lets's calculate LCM of 14,10,77

2 14, 10, 77
7 7, 5, 77
1, 5, 11

∴ So the LCM of the given numbers is 2 x 7 x 1 x 5 x 11 = 770

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/770

Therefore, the GCF of Fractions 67/14,72/10,300/77 is 1/770

Least Common Multiple of 14,10,77 with GCF Formula

Least Common Multiple of 14,10,77 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 14,10,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,10,77) = 1

common factors(in case of two or more numbers have common factors) = 14

GCF(14,10,77) x common factors =1 x 14 = 14

LCM(14,10,77) = ( 14 × 10 × 77 ) / 14

LCM(14,10,77) = 10780 / 14

LCM(14,10,77) = 770


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 67/14, 72/10, 300/77

1. 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.

2. What is the GCF of Fractions for 67/14, 72/10, 300/77?

Answer: GCF of Numerators as per given numbers 67/14, 72/10, 300/77 is

GCF of Numerators i.e. for 67,72,300 is 1

LCM of denominators i.e. for 14,10,77 is 770.

Thus, GCF of Fractions is 1/770.Finally, GCF of Fractions for 67/14, 72/10, 300/77 is 1/770.