GCF of 30/42, 684/40, 874/411
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/42, 684/40, 874/411 i.e 2/115080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/42, 684/40, 874/411.
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 30/42,684/40,874/411?
Given fractions are 30/42,684/40,874/411
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 30/42,684/40,874/411, numerators are 30,684,874
Denominators are 42,40,411
The GCF of 30,684,874 is 2 .
LCM of 42,40,411 is 115080.
The greatest common factor of 30/42,684/40,874/411 = [GCF of 30,684,874]/[LCM of 42,40,411]= 2/115080
Therefore, the GCF of 30/42,684/40,874/411 is 2/115080.
To find the highest common factor of 30,684,874, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The HCF of 30,684,874 is 2.
Lets's calculate GCF of 30,684,874
| 2 | 30, 684, 874 |
| 15, 342, 437 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 30,684,874 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Greatest Common Factor
We found the factors 30,684,874 . The biggest common factor number is the GCF number.
So the greatest common factor 30,684,874 is 2.
Lets's calculate LCM of 42,40,411
| 2 | 42, 40, 411 |
| 3 | 21, 20, 411 |
| 7, 20, 137 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 20 x 137 = 115080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115080
Therefore, the GCF of Fractions 30/42,684/40,874/411 is 2/115080
Least Common Multiple of 42,40,411 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 42,40,411 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,40,411) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(42,40,411) x common factors =1 x 6 = 6
LCM(42,40,411) = ( 42 × 40 × 411 ) / 6
LCM(42,40,411) = 690480 / 6
LCM(42,40,411) = 115080
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 30/42, 684/40, 874/411
1. What is the HCF of 30,684,874?
The HCF of 30,684,874 is 2
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 30/42, 684/40, 874/411?
Answer: GCF of Numerators as per given numbers 30/42, 684/40, 874/411 is
GCF of Numerators i.e. for 30,684,874 is 2
LCM of denominators i.e. for 42,40,411 is 115080.
Thus, GCF of Fractions is 2/115080.Finally, GCF of Fractions for 30/42, 684/40, 874/411 is 2/115080.