GCF of 3/85, 67/22, 59/624, 120/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/85, 67/22, 59/624, 120/546 i.e 1/4084080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/85, 67/22, 59/624, 120/546.
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 3/85,67/22,59/624,120/546?
Given fractions are 3/85,67/22,59/624,120/546
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 3/85,67/22,59/624,120/546, numerators are 3,67,59,120
Denominators are 85,22,624,546
The GCF of 3,67,59,120 is 1 .
LCM of 85,22,624,546 is 4084080.
The greatest common factor of 3/85,67/22,59/624,120/546 = [GCF of 3,67,59,120]/[LCM of 85,22,624,546]= 1/4084080
Therefore, the GCF of 3/85,67/22,59/624,120/546 is 1/4084080.
To find the highest common factor of 3,67,59,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 67 are 1, 67
The factors of 59 are 1, 59
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 3,67,59,120 is 1.
Lets's calculate GCF of 3,67,59,120
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,67,59,120 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 67
:1,67
Now, list down the factors of 59
:1,59
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 3,67,59,120 . The biggest common factor number is the GCF number.
So the greatest common factor 3,67,59,120 is 1.
Lets's calculate LCM of 85,22,624,546
| 2 | 85, 22, 624, 546 |
| 3 | 85, 11, 312, 273 |
| 13 | 85, 11, 104, 91 |
| 85, 11, 8, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 85 x 11 x 8 x 7 = 4084080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4084080
Therefore, the GCF of Fractions 3/85,67/22,59/624,120/546 is 1/4084080
Least Common Multiple of 85,22,624,546 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 85,22,624,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,22,624,546) = 1
common factors(in case of two or more numbers have common factors) = 156
GCF(85,22,624,546) x common factors =1 x 156 = 156
LCM(85,22,624,546) = ( 85 × 22 × 624 × 546 ) / 156
LCM(85,22,624,546) = 637116480 / 156
LCM(85,22,624,546) = 4084080
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3/85, 67/22, 59/624, 120/546
1. What is the HCF of 3,67,59,120?
The HCF of 3,67,59,120 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 3/85, 67/22, 59/624, 120/546?
Answer: GCF of Numerators as per given numbers 3/85, 67/22, 59/624, 120/546 is
GCF of Numerators i.e. for 3,67,59,120 is 1
LCM of denominators i.e. for 85,22,624,546 is 4084080.
Thus, GCF of Fractions is 1/4084080.Finally, GCF of Fractions for 3/85, 67/22, 59/624, 120/546 is 1/4084080.