GCF of 352/78, 272/642
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 352/78, 272/642 i.e 16/8346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 352/78, 272/642.
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 352/78,272/642?
Given fractions are 352/78,272/642
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 352/78,272/642, numerators are 352,272
Denominators are 78,642
The GCF of 352,272 is 16 .
LCM of 78,642 is 8346.
The greatest common factor of 352/78,272/642 = [GCF of 352,272]/[LCM of 78,642]= 16/8346
Therefore, the GCF of 352/78,272/642 is 16/8346.
To find the highest common factor of 352,272, we have to find the factors of both numbers and list the highest common factor.
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
The HCF of 352,272 is 16.
Lets's calculate GCF of 352,272
| 2 | 352, 272 |
| 2 | 176, 136 |
| 2 | 88, 68 |
| 2 | 44, 34 |
| 22, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 352,272 By Matching Biggest Common Factor Method
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
Greatest Common Factor
We found the factors 352,272 . The biggest common factor number is the GCF number.
So the greatest common factor 352,272 is 16.
Lets's calculate LCM of 78,642
| 2 | 78, 642 |
| 3 | 39, 321 |
| 13, 107 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 107 = 8346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/8346
Therefore, the GCF of Fractions 352/78,272/642 is 16/8346
Least Common Multiple of 78,642 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 78,642 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,642) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(78,642) x common factors =6 x 1 = 6
LCM(78,642) = ( 78 × 642 ) / 6
LCM(78,642) = 50076 / 6
LCM(78,642) = 8346
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FAQs on GCF of Fractions of 352/78, 272/642
1. What is the HCF of 352,272?
The HCF of 352,272 is 16
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 352/78, 272/642?
Answer: GCF of Numerators as per given numbers 352/78, 272/642 is
GCF of Numerators i.e. for 352,272 is 16
LCM of denominators i.e. for 78,642 is 8346.
Thus, GCF of Fractions is 16/8346.Finally, GCF of Fractions for 352/78, 272/642 is 16/8346.