GCF of 1/43, 78/77, 30/954, 400/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1/43, 78/77, 30/954, 400/412 i.e 1/650690964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/43, 78/77, 30/954, 400/412.
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 1/43,78/77,30/954,400/412?
Given fractions are 1/43,78/77,30/954,400/412
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 1/43,78/77,30/954,400/412, numerators are 1,78,30,400
Denominators are 43,77,954,412
The GCF of 1,78,30,400 is 1 .
LCM of 43,77,954,412 is 650690964.
The greatest common factor of 1/43,78/77,30/954,400/412 = [GCF of 1,78,30,400]/[LCM of 43,77,954,412]= 1/650690964
Therefore, the GCF of 1/43,78/77,30/954,400/412 is 1/650690964.
To find the highest common factor of 1,78,30,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 1 are 1
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 1,78,30,400 is 1.
Lets's calculate GCF of 1,78,30,400
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1,78,30,400 By Matching Biggest Common Factor Method
Now, list down the factors of 1
:1
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 1,78,30,400 . The biggest common factor number is the GCF number.
So the greatest common factor 1,78,30,400 is 1.
Lets's calculate LCM of 43,77,954,412
| 2 | 43, 77, 954, 412 |
| 43, 77, 477, 206 |
∴ So the LCM of the given numbers is 2 x 43 x 77 x 477 x 206 = 650690964
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/650690964
Therefore, the GCF of Fractions 1/43,78/77,30/954,400/412 is 1/650690964
Least Common Multiple of 43,77,954,412 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 43,77,954,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(43,77,954,412) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(43,77,954,412) x common factors =1 x 2 = 2
LCM(43,77,954,412) = ( 43 × 77 × 954 × 412 ) / 2
LCM(43,77,954,412) = 1301381928 / 2
LCM(43,77,954,412) = 650690964
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 1/43, 78/77, 30/954, 400/412
1. What is the HCF of 1,78,30,400?
The HCF of 1,78,30,400 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 1/43, 78/77, 30/954, 400/412?
Answer: GCF of Numerators as per given numbers 1/43, 78/77, 30/954, 400/412 is
GCF of Numerators i.e. for 1,78,30,400 is 1
LCM of denominators i.e. for 43,77,954,412 is 650690964.
Thus, GCF of Fractions is 1/650690964.Finally, GCF of Fractions for 1/43, 78/77, 30/954, 400/412 is 1/650690964.