GCF of 167/224, 320/509
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 167/224, 320/509 i.e 1/114016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 167/224, 320/509.
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 167/224,320/509?
Given fractions are 167/224,320/509
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 167/224,320/509, numerators are 167,320
Denominators are 224,509
The GCF of 167,320 is 1 .
LCM of 224,509 is 114016.
The greatest common factor of 167/224,320/509 = [GCF of 167,320]/[LCM of 224,509]= 1/114016
Therefore, the GCF of 167/224,320/509 is 1/114016.
To find the highest common factor of 167,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 167 are 1, 167
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 167,320 is 1.
Lets's calculate GCF of 167,320
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 167,320 By Matching Biggest Common Factor Method
Now, list down the factors of 167
:1,167
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 167,320 . The biggest common factor number is the GCF number.
So the greatest common factor 167,320 is 1.
Lets's calculate LCM of 224,509
Given numbers has no common factors except 1. So, there LCM is their product i.e 114016
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/114016
Therefore, the GCF of Fractions 167/224,320/509 is 1/114016
Least Common Multiple of 224,509 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 224,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,509) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(224,509) x common factors =1 x 1 = 1
LCM(224,509) = ( 224 × 509 ) / 1
LCM(224,509) = 114016 / 1
LCM(224,509) = 114016
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FAQs on GCF of Fractions of 167/224, 320/509
1. What is the HCF of 167,320?
The HCF of 167,320 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 167/224, 320/509?
Answer: GCF of Numerators as per given numbers 167/224, 320/509 is
GCF of Numerators i.e. for 167,320 is 1
LCM of denominators i.e. for 224,509 is 114016.
Thus, GCF of Fractions is 1/114016.Finally, GCF of Fractions for 167/224, 320/509 is 1/114016.