GCF of 173/480, 420/342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 173/480, 420/342 i.e 1/27360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 173/480, 420/342.
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 173/480,420/342?
Given fractions are 173/480,420/342
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 173/480,420/342, numerators are 173,420
Denominators are 480,342
The GCF of 173,420 is 1 .
LCM of 480,342 is 27360.
The greatest common factor of 173/480,420/342 = [GCF of 173,420]/[LCM of 480,342]= 1/27360
Therefore, the GCF of 173/480,420/342 is 1/27360.
To find the highest common factor of 173,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 173 are 1, 173
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 173,420 is 1.
Lets's calculate GCF of 173,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 173,420 By Matching Biggest Common Factor Method
Now, list down the factors of 173
:1,173
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 173,420 . The biggest common factor number is the GCF number.
So the greatest common factor 173,420 is 1.
Lets's calculate LCM of 480,342
| 2 | 480, 342 |
| 3 | 240, 171 |
| 80, 57 |
∴ So the LCM of the given numbers is 2 x 3 x 80 x 57 = 27360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27360
Therefore, the GCF of Fractions 173/480,420/342 is 1/27360
Least Common Multiple of 480,342 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 480,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(480,342) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(480,342) x common factors =6 x 1 = 6
LCM(480,342) = ( 480 × 342 ) / 6
LCM(480,342) = 164160 / 6
LCM(480,342) = 27360
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FAQs on GCF of Fractions of 173/480, 420/342
1. What is the HCF of 173,420?
The HCF of 173,420 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 173/480, 420/342?
Answer: GCF of Numerators as per given numbers 173/480, 420/342 is
GCF of Numerators i.e. for 173,420 is 1
LCM of denominators i.e. for 480,342 is 27360.
Thus, GCF of Fractions is 1/27360.Finally, GCF of Fractions for 173/480, 420/342 is 1/27360.