GCF of 37/31, 22/51, 77/40, 36/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 37/31, 22/51, 77/40, 36/84 i.e 1/442680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 37/31, 22/51, 77/40, 36/84.
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 37/31,22/51,77/40,36/84?
Given fractions are 37/31,22/51,77/40,36/84
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 37/31,22/51,77/40,36/84, numerators are 37,22,77,36
Denominators are 31,51,40,84
The GCF of 37,22,77,36 is 1 .
LCM of 31,51,40,84 is 442680.
The greatest common factor of 37/31,22/51,77/40,36/84 = [GCF of 37,22,77,36]/[LCM of 31,51,40,84]= 1/442680
Therefore, the GCF of 37/31,22/51,77/40,36/84 is 1/442680.
To find the highest common factor of 37,22,77,36, we have to find the factors of both numbers and list the highest common factor.
The factors of 37 are 1, 37
The factors of 22 are 1, 2, 11, 22
The factors of 77 are 1, 7, 11, 77
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF of 37,22,77,36 is 1.
Lets's calculate GCF of 37,22,77,36
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 37,22,77,36 By Matching Biggest Common Factor Method
Now, list down the factors of 37
:1,37
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Greatest Common Factor
We found the factors 37,22,77,36 . The biggest common factor number is the GCF number.
So the greatest common factor 37,22,77,36 is 1.
Lets's calculate LCM of 31,51,40,84
| 2 | 31, 51, 40, 84 |
| 2 | 31, 51, 20, 42 |
| 3 | 31, 51, 10, 21 |
| 31, 17, 10, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 31 x 17 x 10 x 7 = 442680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/442680
Therefore, the GCF of Fractions 37/31,22/51,77/40,36/84 is 1/442680
Least Common Multiple of 31,51,40,84 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 31,51,40,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,51,40,84) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(31,51,40,84) x common factors =1 x 12 = 12
LCM(31,51,40,84) = ( 31 × 51 × 40 × 84 ) / 12
LCM(31,51,40,84) = 5312160 / 12
LCM(31,51,40,84) = 442680
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 37/31, 22/51, 77/40, 36/84
1. What is the HCF of 37,22,77,36?
The HCF of 37,22,77,36 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 37/31, 22/51, 77/40, 36/84?
Answer: GCF of Numerators as per given numbers 37/31, 22/51, 77/40, 36/84 is
GCF of Numerators i.e. for 37,22,77,36 is 1
LCM of denominators i.e. for 31,51,40,84 is 442680.
Thus, GCF of Fractions is 1/442680.Finally, GCF of Fractions for 37/31, 22/51, 77/40, 36/84 is 1/442680.