GCF of 87/56, 84/40, 23/40, 76/58
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 87/56, 84/40, 23/40, 76/58 i.e 1/8120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/56, 84/40, 23/40, 76/58.
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 87/56,84/40,23/40,76/58?
Given fractions are 87/56,84/40,23/40,76/58
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 87/56,84/40,23/40,76/58, numerators are 87,84,23,76
Denominators are 56,40,40,58
The GCF of 87,84,23,76 is 1 .
LCM of 56,40,40,58 is 8120.
The greatest common factor of 87/56,84/40,23/40,76/58 = [GCF of 87,84,23,76]/[LCM of 56,40,40,58]= 1/8120
Therefore, the GCF of 87/56,84/40,23/40,76/58 is 1/8120.
To find the highest common factor of 87,84,23,76, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 23 are 1, 23
The factors of 76 are 1, 2, 4, 19, 38, 76
The HCF of 87,84,23,76 is 1.
Lets's calculate GCF of 87,84,23,76
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 87,84,23,76 By Matching Biggest Common Factor Method
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 23
:1,23
Now, list down the factors of 76
:1,2,4,19,38,76
Greatest Common Factor
We found the factors 87,84,23,76 . The biggest common factor number is the GCF number.
So the greatest common factor 87,84,23,76 is 1.
Lets's calculate LCM of 56,40,40,58
| 2 | 56, 40, 40, 58 |
| 2 | 28, 20, 20, 29 |
| 2 | 14, 10, 10, 29 |
| 5 | 7, 5, 5, 29 |
| 7, 1, 1, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 7 x 1 x 1 x 29 = 8120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8120
Therefore, the GCF of Fractions 87/56,84/40,23/40,76/58 is 1/8120
Least Common Multiple of 56,40,40,58 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 56,40,40,58 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,40,40,58) = 2
common factors(in case of two or more numbers have common factors) = 320
GCF(56,40,40,58) x common factors =2 x 320 = 640
LCM(56,40,40,58) = ( 56 × 40 × 40 × 58 ) / 640
LCM(56,40,40,58) = 5196800 / 640
LCM(56,40,40,58) = 8120
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 87/56, 84/40, 23/40, 76/58
1. What is the HCF of 87,84,23,76?
The HCF of 87,84,23,76 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 87/56, 84/40, 23/40, 76/58?
Answer: GCF of Numerators as per given numbers 87/56, 84/40, 23/40, 76/58 is
GCF of Numerators i.e. for 87,84,23,76 is 1
LCM of denominators i.e. for 56,40,40,58 is 8120.
Thus, GCF of Fractions is 1/8120.Finally, GCF of Fractions for 87/56, 84/40, 23/40, 76/58 is 1/8120.