GCF of 30/706, 94/416, 749/871
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/706, 94/416, 749/871 i.e 1/9838816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/706, 94/416, 749/871.
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 30/706,94/416,749/871?
Given fractions are 30/706,94/416,749/871
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 30/706,94/416,749/871, numerators are 30,94,749
Denominators are 706,416,871
The GCF of 30,94,749 is 1 .
LCM of 706,416,871 is 9838816.
The greatest common factor of 30/706,94/416,749/871 = [GCF of 30,94,749]/[LCM of 706,416,871]= 1/9838816
Therefore, the GCF of 30/706,94/416,749/871 is 1/9838816.
To find the highest common factor of 30,94,749, 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 94 are 1, 2, 47, 94
The factors of 749 are 1, 7, 107, 749
The HCF of 30,94,749 is 1.
Lets's calculate GCF of 30,94,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,94,749 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 94
:1,2,47,94
Now, list down the factors of 749
:1,7,107,749
Greatest Common Factor
We found the factors 30,94,749 . The biggest common factor number is the GCF number.
So the greatest common factor 30,94,749 is 1.
Lets's calculate LCM of 706,416,871
| 2 | 706, 416, 871 |
| 13 | 353, 208, 871 |
| 353, 16, 67 |
∴ So the LCM of the given numbers is 2 x 13 x 353 x 16 x 67 = 9838816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9838816
Therefore, the GCF of Fractions 30/706,94/416,749/871 is 1/9838816
Least Common Multiple of 706,416,871 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 706,416,871 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,416,871) = 1
common factors(in case of two or more numbers have common factors) = 26
GCF(706,416,871) x common factors =1 x 26 = 26
LCM(706,416,871) = ( 706 × 416 × 871 ) / 26
LCM(706,416,871) = 255809216 / 26
LCM(706,416,871) = 9838816
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FAQs on GCF of Fractions of 30/706, 94/416, 749/871
1. What is the HCF of 30,94,749?
The HCF of 30,94,749 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 30/706, 94/416, 749/871?
Answer: GCF of Numerators as per given numbers 30/706, 94/416, 749/871 is
GCF of Numerators i.e. for 30,94,749 is 1
LCM of denominators i.e. for 706,416,871 is 9838816.
Thus, GCF of Fractions is 1/9838816.Finally, GCF of Fractions for 30/706, 94/416, 749/871 is 1/9838816.