GCF of 604/60, 294/37, 420/14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 604/60, 294/37, 420/14 i.e 2/15540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 604/60, 294/37, 420/14.
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 604/60,294/37,420/14?
Given fractions are 604/60,294/37,420/14
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 604/60,294/37,420/14, numerators are 604,294,420
Denominators are 60,37,14
The GCF of 604,294,420 is 2 .
LCM of 60,37,14 is 15540.
The greatest common factor of 604/60,294/37,420/14 = [GCF of 604,294,420]/[LCM of 60,37,14]= 2/15540
Therefore, the GCF of 604/60,294/37,420/14 is 2/15540.
To find the highest common factor of 604,294,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 604 are 1, 2, 4, 151, 302, 604
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
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 604,294,420 is 2.
Lets's calculate GCF of 604,294,420
| 2 | 604, 294, 420 |
| 302, 147, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 604,294,420 By Matching Biggest Common Factor Method
Now, list down the factors of 604
:1,2,4,151,302,604
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
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 604,294,420 . The biggest common factor number is the GCF number.
So the greatest common factor 604,294,420 is 2.
Lets's calculate LCM of 60,37,14
| 2 | 60, 37, 14 |
| 30, 37, 7 |
∴ So the LCM of the given numbers is 2 x 30 x 37 x 7 = 15540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15540
Therefore, the GCF of Fractions 604/60,294/37,420/14 is 2/15540
Least Common Multiple of 60,37,14 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 60,37,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,37,14) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(60,37,14) x common factors =1 x 2 = 2
LCM(60,37,14) = ( 60 × 37 × 14 ) / 2
LCM(60,37,14) = 31080 / 2
LCM(60,37,14) = 15540
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FAQs on GCF of Fractions of 604/60, 294/37, 420/14
1. What is the HCF of 604,294,420?
The HCF of 604,294,420 is 2
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 604/60, 294/37, 420/14?
Answer: GCF of Numerators as per given numbers 604/60, 294/37, 420/14 is
GCF of Numerators i.e. for 604,294,420 is 2
LCM of denominators i.e. for 60,37,14 is 15540.
Thus, GCF of Fractions is 2/15540.Finally, GCF of Fractions for 604/60, 294/37, 420/14 is 2/15540.