GCF of 3/42, 21/34, 78/660, 900/211
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/42, 21/34, 78/660, 900/211 i.e 3/16571940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/42, 21/34, 78/660, 900/211.
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 3/42,21/34,78/660,900/211?
Given fractions are 3/42,21/34,78/660,900/211
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 3/42,21/34,78/660,900/211, numerators are 3,21,78,900
Denominators are 42,34,660,211
The GCF of 3,21,78,900 is 3 .
LCM of 42,34,660,211 is 16571940.
The greatest common factor of 3/42,21/34,78/660,900/211 = [GCF of 3,21,78,900]/[LCM of 42,34,660,211]= 3/16571940
Therefore, the GCF of 3/42,21/34,78/660,900/211 is 3/16571940.
To find the highest common factor of 3,21,78,900, 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 21 are 1, 3, 7, 21
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The HCF of 3,21,78,900 is 3.
Lets's calculate GCF of 3,21,78,900
| 3 | 3, 21, 78, 900 |
| 1, 7, 26, 300 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3,21,78,900 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Greatest Common Factor
We found the factors 3,21,78,900 . The biggest common factor number is the GCF number.
So the greatest common factor 3,21,78,900 is 3.
Lets's calculate LCM of 42,34,660,211
| 2 | 42, 34, 660, 211 |
| 3 | 21, 17, 330, 211 |
| 7, 17, 110, 211 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 17 x 110 x 211 = 16571940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/16571940
Therefore, the GCF of Fractions 3/42,21/34,78/660,900/211 is 3/16571940
Least Common Multiple of 42,34,660,211 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 42,34,660,211 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,34,660,211) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(42,34,660,211) x common factors =1 x 12 = 12
LCM(42,34,660,211) = ( 42 × 34 × 660 × 211 ) / 12
LCM(42,34,660,211) = 198863280 / 12
LCM(42,34,660,211) = 16571940
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3/42, 21/34, 78/660, 900/211
1. What is the HCF of 3,21,78,900?
The HCF of 3,21,78,900 is 3
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 3/42, 21/34, 78/660, 900/211?
Answer: GCF of Numerators as per given numbers 3/42, 21/34, 78/660, 900/211 is
GCF of Numerators i.e. for 3,21,78,900 is 3
LCM of denominators i.e. for 42,34,660,211 is 16571940.
Thus, GCF of Fractions is 3/16571940.Finally, GCF of Fractions for 3/42, 21/34, 78/660, 900/211 is 3/16571940.