GCF of 378/42, 372/1680
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/42, 372/1680 i.e 6/1680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/42, 372/1680.
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 378/42,372/1680?
Given fractions are 378/42,372/1680
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 378/42,372/1680, numerators are 378,372
Denominators are 42,1680
The GCF of 378,372 is 6 .
LCM of 42,1680 is 1680.
The greatest common factor of 378/42,372/1680 = [GCF of 378,372]/[LCM of 42,1680]= 6/1680
Therefore, the GCF of 378/42,372/1680 is 6/1680.
To find the highest common factor of 378,372, 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 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372
The HCF of 378,372 is 6.
Lets's calculate GCF of 378,372
| 2 | 378, 372 |
| 3 | 189, 186 |
| 63, 62 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 378,372 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 372
:1,2,3,4,6,12,31,62,93,124,186,372
Greatest Common Factor
We found the factors 378,372 . The biggest common factor number is the GCF number.
So the greatest common factor 378,372 is 6.
Lets's calculate LCM of 42,1680
| 2 | 42, 1680 |
| 3 | 21, 840 |
| 7 | 7, 280 |
| 1, 40 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 40 = 1680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1680
Therefore, the GCF of Fractions 378/42,372/1680 is 6/1680
Least Common Multiple of 42,1680 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 42,1680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,1680) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(42,1680) x common factors =42 x 1 = 42
LCM(42,1680) = ( 42 × 1680 ) / 42
LCM(42,1680) = 70560 / 42
LCM(42,1680) = 1680
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FAQs on GCF of Fractions of 378/42, 372/1680
1. What is the HCF of 378,372?
The HCF of 378,372 is 6
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 378/42, 372/1680?
Answer: GCF of Numerators as per given numbers 378/42, 372/1680 is
GCF of Numerators i.e. for 378,372 is 6
LCM of denominators i.e. for 42,1680 is 1680.
Thus, GCF of Fractions is 6/1680.Finally, GCF of Fractions for 378/42, 372/1680 is 6/1680.