GCF of 378/28, 882/6972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/28, 882/6972 i.e 126/6972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/28, 882/6972.
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 378/28,882/6972?
Given fractions are 378/28,882/6972
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 378/28,882/6972, numerators are 378,882
Denominators are 28,6972
The GCF of 378,882 is 126 .
LCM of 28,6972 is 6972.
The greatest common factor of 378/28,882/6972 = [GCF of 378,882]/[LCM of 28,6972]= 126/6972
Therefore, the GCF of 378/28,882/6972 is 126/6972.
To find the highest common factor of 378,882, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 882 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
The HCF of 378,882 is 126.
Lets's calculate GCF of 378,882
| 2 | 378, 882 |
| 3 | 189, 441 |
| 3 | 63, 147 |
| 7 | 21, 49 |
| 3, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 7 = 126
Greatest Common Factor of 378,882 By Matching Biggest Common Factor Method
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 882
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,441,882
Greatest Common Factor
We found the factors 378,882 . The biggest common factor number is the GCF number.
So the greatest common factor 378,882 is 126.
Lets's calculate LCM of 28,6972
| 2 | 28, 6972 |
| 2 | 14, 3486 |
| 7 | 7, 1743 |
| 1, 249 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 1 x 249 = 6972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 126/6972
Therefore, the GCF of Fractions 378/28,882/6972 is 126/6972
Least Common Multiple of 28,6972 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 28,6972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,6972) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(28,6972) x common factors =28 x 1 = 28
LCM(28,6972) = ( 28 × 6972 ) / 28
LCM(28,6972) = 195216 / 28
LCM(28,6972) = 6972
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FAQs on GCF of Fractions of 378/28, 882/6972
1. What is the HCF of 378,882?
The HCF of 378,882 is 126
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 378/28, 882/6972?
Answer: GCF of Numerators as per given numbers 378/28, 882/6972 is
GCF of Numerators i.e. for 378,882 is 126
LCM of denominators i.e. for 28,6972 is 6972.
Thus, GCF of Fractions is 126/6972.Finally, GCF of Fractions for 378/28, 882/6972 is 126/6972.