GCF of 36/43, 10/84, 35/30, 49/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 36/43, 10/84, 35/30, 49/21 i.e 1/18060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/43, 10/84, 35/30, 49/21.
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 36/43,10/84,35/30,49/21?
Given fractions are 36/43,10/84,35/30,49/21
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 36/43,10/84,35/30,49/21, numerators are 36,10,35,49
Denominators are 43,84,30,21
The GCF of 36,10,35,49 is 1 .
LCM of 43,84,30,21 is 18060.
The greatest common factor of 36/43,10/84,35/30,49/21 = [GCF of 36,10,35,49]/[LCM of 43,84,30,21]= 1/18060
Therefore, the GCF of 36/43,10/84,35/30,49/21 is 1/18060.
To find the highest common factor of 36,10,35,49, we have to find the factors of both numbers and list the highest common factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 10 are 1, 2, 5, 10
The factors of 35 are 1, 5, 7, 35
The factors of 49 are 1, 7, 49
The HCF of 36,10,35,49 is 1.
Lets's calculate GCF of 36,10,35,49
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 36,10,35,49 By Matching Biggest Common Factor Method
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 49
:1,7,49
Greatest Common Factor
We found the factors 36,10,35,49 . The biggest common factor number is the GCF number.
So the greatest common factor 36,10,35,49 is 1.
Lets's calculate LCM of 43,84,30,21
| 2 | 43, 84, 30, 21 |
| 3 | 43, 42, 15, 21 |
| 7 | 43, 14, 5, 7 |
| 43, 2, 5, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 43 x 2 x 5 x 1 = 18060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18060
Therefore, the GCF of Fractions 36/43,10/84,35/30,49/21 is 1/18060
Least Common Multiple of 43,84,30,21 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 43,84,30,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(43,84,30,21) = 1
common factors(in case of two or more numbers have common factors) = 126
GCF(43,84,30,21) x common factors =1 x 126 = 126
LCM(43,84,30,21) = ( 43 × 84 × 30 × 21 ) / 126
LCM(43,84,30,21) = 2275560 / 126
LCM(43,84,30,21) = 18060
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 36/43, 10/84, 35/30, 49/21
1. What is the HCF of 36,10,35,49?
The HCF of 36,10,35,49 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 36/43, 10/84, 35/30, 49/21?
Answer: GCF of Numerators as per given numbers 36/43, 10/84, 35/30, 49/21 is
GCF of Numerators i.e. for 36,10,35,49 is 1
LCM of denominators i.e. for 43,84,30,21 is 18060.
Thus, GCF of Fractions is 1/18060.Finally, GCF of Fractions for 36/43, 10/84, 35/30, 49/21 is 1/18060.