GCF of 5430/680, 8370/8778
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5430/680, 8370/8778 i.e 30/2984520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5430/680, 8370/8778.
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 5430/680,8370/8778?
Given fractions are 5430/680,8370/8778
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 5430/680,8370/8778, numerators are 5430,8370
Denominators are 680,8778
The GCF of 5430,8370 is 30 .
LCM of 680,8778 is 2984520.
The greatest common factor of 5430/680,8370/8778 = [GCF of 5430,8370]/[LCM of 680,8778]= 30/2984520
Therefore, the GCF of 5430/680,8370/8778 is 30/2984520.
To find the highest common factor of 5430,8370, we have to find the factors of both numbers and list the highest common factor.
The factors of 5430 are 1, 2, 3, 5, 6, 10, 15, 30, 181, 362, 543, 905, 1086, 1810, 2715, 5430
The factors of 8370 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 31, 45, 54, 62, 90, 93, 135, 155, 186, 270, 279, 310, 465, 558, 837, 930, 1395, 1674, 2790, 4185, 8370
The HCF of 5430,8370 is 30.
Lets's calculate GCF of 5430,8370
| 2 | 5430, 8370 |
| 3 | 2715, 4185 |
| 5 | 905, 1395 |
| 181, 279 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 5430,8370 By Matching Biggest Common Factor Method
Now, list down the factors of 5430
:1,2,3,5,6,10,15,30,181,362,543,905,1086,1810,2715,5430
Now, list down the factors of 8370
:1,2,3,5,6,9,10,15,18,27,30,31,45,54,62,90,93,135,155,186,270,279,310,465,558,837,930,1395,1674,2790,4185,8370
Greatest Common Factor
We found the factors 5430,8370 . The biggest common factor number is the GCF number.
So the greatest common factor 5430,8370 is 30.
Lets's calculate LCM of 680,8778
| 2 | 680, 8778 |
| 340, 4389 |
∴ So the LCM of the given numbers is 2 x 340 x 4389 = 2984520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/2984520
Therefore, the GCF of Fractions 5430/680,8370/8778 is 30/2984520
Least Common Multiple of 680,8778 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 680,8778 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,8778) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(680,8778) x common factors =2 x 1 = 2
LCM(680,8778) = ( 680 × 8778 ) / 2
LCM(680,8778) = 5969040 / 2
LCM(680,8778) = 2984520
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FAQs on GCF of Fractions of 5430/680, 8370/8778
1. What is the HCF of 5430,8370?
The HCF of 5430,8370 is 30
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 5430/680, 8370/8778?
Answer: GCF of Numerators as per given numbers 5430/680, 8370/8778 is
GCF of Numerators i.e. for 5430,8370 is 30
LCM of denominators i.e. for 680,8778 is 2984520.
Thus, GCF of Fractions is 30/2984520.Finally, GCF of Fractions for 5430/680, 8370/8778 is 30/2984520.