GCF of 1330/28, 1672/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1330/28, 1672/678 i.e 38/9492 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1330/28, 1672/678.
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 1330/28,1672/678?
Given fractions are 1330/28,1672/678
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 1330/28,1672/678, numerators are 1330,1672
Denominators are 28,678
The GCF of 1330,1672 is 38 .
LCM of 28,678 is 9492.
The greatest common factor of 1330/28,1672/678 = [GCF of 1330,1672]/[LCM of 28,678]= 38/9492
Therefore, the GCF of 1330/28,1672/678 is 38/9492.
To find the highest common factor of 1330,1672, we have to find the factors of both numbers and list the highest common factor.
The factors of 1330 are 1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330
The factors of 1672 are 1, 2, 4, 8, 11, 19, 22, 38, 44, 76, 88, 152, 209, 418, 836, 1672
The HCF of 1330,1672 is 38.
Lets's calculate GCF of 1330,1672
| 2 | 1330, 1672 |
| 19 | 665, 836 |
| 35, 44 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 1330,1672 By Matching Biggest Common Factor Method
Now, list down the factors of 1330
:1,2,5,7,10,14,19,35,38,70,95,133,190,266,665,1330
Now, list down the factors of 1672
:1,2,4,8,11,19,22,38,44,76,88,152,209,418,836,1672
Greatest Common Factor
We found the factors 1330,1672 . The biggest common factor number is the GCF number.
So the greatest common factor 1330,1672 is 38.
Lets's calculate LCM of 28,678
| 2 | 28, 678 |
| 14, 339 |
∴ So the LCM of the given numbers is 2 x 14 x 339 = 9492
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/9492
Therefore, the GCF of Fractions 1330/28,1672/678 is 38/9492
Least Common Multiple of 28,678 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 28,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(28,678) x common factors =2 x 1 = 2
LCM(28,678) = ( 28 × 678 ) / 2
LCM(28,678) = 18984 / 2
LCM(28,678) = 9492
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FAQs on GCF of Fractions of 1330/28, 1672/678
1. What is the HCF of 1330,1672?
The HCF of 1330,1672 is 38
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 1330/28, 1672/678?
Answer: GCF of Numerators as per given numbers 1330/28, 1672/678 is
GCF of Numerators i.e. for 1330,1672 is 38
LCM of denominators i.e. for 28,678 is 9492.
Thus, GCF of Fractions is 38/9492.Finally, GCF of Fractions for 1330/28, 1672/678 is 38/9492.