GCF of 120/82, 907/4214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 120/82, 907/4214 i.e 1/172774 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/82, 907/4214.
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 120/82,907/4214?
Given fractions are 120/82,907/4214
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 120/82,907/4214, numerators are 120,907
Denominators are 82,4214
The GCF of 120,907 is 1 .
LCM of 82,4214 is 172774.
The greatest common factor of 120/82,907/4214 = [GCF of 120,907]/[LCM of 82,4214]= 1/172774
Therefore, the GCF of 120/82,907/4214 is 1/172774.
To find the highest common factor of 120,907, we have to find the factors of both numbers and list the highest common factor.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 907 are 1, 907
The HCF of 120,907 is 1.
Lets's calculate GCF of 120,907
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 120,907 By Matching Biggest Common Factor Method
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Now, list down the factors of 907
:1,907
Greatest Common Factor
We found the factors 120,907 . The biggest common factor number is the GCF number.
So the greatest common factor 120,907 is 1.
Lets's calculate LCM of 82,4214
| 2 | 82, 4214 |
| 41, 2107 |
∴ So the LCM of the given numbers is 2 x 41 x 2107 = 172774
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/172774
Therefore, the GCF of Fractions 120/82,907/4214 is 1/172774
Least Common Multiple of 82,4214 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 82,4214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,4214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,4214) x common factors =2 x 1 = 2
LCM(82,4214) = ( 82 × 4214 ) / 2
LCM(82,4214) = 345548 / 2
LCM(82,4214) = 172774
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FAQs on GCF of Fractions of 120/82, 907/4214
1. What is the HCF of 120,907?
The HCF of 120,907 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 120/82, 907/4214?
Answer: GCF of Numerators as per given numbers 120/82, 907/4214 is
GCF of Numerators i.e. for 120,907 is 1
LCM of denominators i.e. for 82,4214 is 172774.
Thus, GCF of Fractions is 1/172774.Finally, GCF of Fractions for 120/82, 907/4214 is 1/172774.