GCF of 38/392, 35/104, 221/672
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/392, 35/104, 221/672 i.e 1/61152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/392, 35/104, 221/672.
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 38/392,35/104,221/672?
Given fractions are 38/392,35/104,221/672
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 38/392,35/104,221/672, numerators are 38,35,221
Denominators are 392,104,672
The GCF of 38,35,221 is 1 .
LCM of 392,104,672 is 61152.
The greatest common factor of 38/392,35/104,221/672 = [GCF of 38,35,221]/[LCM of 392,104,672]= 1/61152
Therefore, the GCF of 38/392,35/104,221/672 is 1/61152.
To find the highest common factor of 38,35,221, we have to find the factors of both numbers and list the highest common factor.
The factors of 38 are 1, 2, 19, 38
The factors of 35 are 1, 5, 7, 35
The factors of 221 are 1, 13, 17, 221
The HCF of 38,35,221 is 1.
Lets's calculate GCF of 38,35,221
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 38,35,221 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 221
:1,13,17,221
Greatest Common Factor
We found the factors 38,35,221 . The biggest common factor number is the GCF number.
So the greatest common factor 38,35,221 is 1.
Lets's calculate LCM of 392,104,672
| 2 | 392, 104, 672 |
| 2 | 196, 52, 336 |
| 2 | 98, 26, 168 |
| 7 | 49, 13, 84 |
| 7, 13, 12 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 7 x 13 x 12 = 61152
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61152
Therefore, the GCF of Fractions 38/392,35/104,221/672 is 1/61152
Least Common Multiple of 392,104,672 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 392,104,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(392,104,672) = 8
common factors(in case of two or more numbers have common factors) = 56
GCF(392,104,672) x common factors =8 x 56 = 448
LCM(392,104,672) = ( 392 × 104 × 672 ) / 448
LCM(392,104,672) = 27396096 / 448
LCM(392,104,672) = 61152
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FAQs on GCF of Fractions of 38/392, 35/104, 221/672
1. What is the HCF of 38,35,221?
The HCF of 38,35,221 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 38/392, 35/104, 221/672?
Answer: GCF of Numerators as per given numbers 38/392, 35/104, 221/672 is
GCF of Numerators i.e. for 38,35,221 is 1
LCM of denominators i.e. for 392,104,672 is 61152.
Thus, GCF of Fractions is 1/61152.Finally, GCF of Fractions for 38/392, 35/104, 221/672 is 1/61152.