GCF of 709/312, 380/149
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 709/312, 380/149 i.e 1/46488 easily. The following is the detailed procedure to determine the greatest common factor of fractions 709/312, 380/149.
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 709/312,380/149?
Given fractions are 709/312,380/149
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 709/312,380/149, numerators are 709,380
Denominators are 312,149
The GCF of 709,380 is 1 .
LCM of 312,149 is 46488.
The greatest common factor of 709/312,380/149 = [GCF of 709,380]/[LCM of 312,149]= 1/46488
Therefore, the GCF of 709/312,380/149 is 1/46488.
To find the highest common factor of 709,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 709 are 1, 709
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 709,380 is 1.
Lets's calculate GCF of 709,380
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 709,380 By Matching Biggest Common Factor Method
Now, list down the factors of 709
:1,709
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 709,380 . The biggest common factor number is the GCF number.
So the greatest common factor 709,380 is 1.
Lets's calculate LCM of 312,149
Given numbers has no common factors except 1. So, there LCM is their product i.e 46488
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/46488
Therefore, the GCF of Fractions 709/312,380/149 is 1/46488
Least Common Multiple of 312,149 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 312,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,149) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(312,149) x common factors =1 x 1 = 1
LCM(312,149) = ( 312 × 149 ) / 1
LCM(312,149) = 46488 / 1
LCM(312,149) = 46488
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FAQs on GCF of Fractions of 709/312, 380/149
1. What is the HCF of 709,380?
The HCF of 709,380 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 709/312, 380/149?
Answer: GCF of Numerators as per given numbers 709/312, 380/149 is
GCF of Numerators i.e. for 709,380 is 1
LCM of denominators i.e. for 312,149 is 46488.
Thus, GCF of Fractions is 1/46488.Finally, GCF of Fractions for 709/312, 380/149 is 1/46488.