GCF of 28/178, 1470/7002
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/178, 1470/7002 i.e 14/623178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/178, 1470/7002.
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 28/178,1470/7002?
Given fractions are 28/178,1470/7002
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 28/178,1470/7002, numerators are 28,1470
Denominators are 178,7002
The GCF of 28,1470 is 14 .
LCM of 178,7002 is 623178.
The greatest common factor of 28/178,1470/7002 = [GCF of 28,1470]/[LCM of 178,7002]= 14/623178
Therefore, the GCF of 28/178,1470/7002 is 14/623178.
To find the highest common factor of 28,1470, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470
The HCF of 28,1470 is 14.
Lets's calculate GCF of 28,1470
| 2 | 28, 1470 |
| 7 | 14, 735 |
| 2, 105 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 28,1470 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 1470
:1,2,3,5,6,7,10,14,15,21,30,35,42,49,70,98,105,147,210,245,294,490,735,1470
Greatest Common Factor
We found the factors 28,1470 . The biggest common factor number is the GCF number.
So the greatest common factor 28,1470 is 14.
Lets's calculate LCM of 178,7002
| 2 | 178, 7002 |
| 89, 3501 |
∴ So the LCM of the given numbers is 2 x 89 x 3501 = 623178
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/623178
Therefore, the GCF of Fractions 28/178,1470/7002 is 14/623178
Least Common Multiple of 178,7002 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 178,7002 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,7002) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,7002) x common factors =2 x 1 = 2
LCM(178,7002) = ( 178 × 7002 ) / 2
LCM(178,7002) = 1246356 / 2
LCM(178,7002) = 623178
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FAQs on GCF of Fractions of 28/178, 1470/7002
1. What is the HCF of 28,1470?
The HCF of 28,1470 is 14
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 28/178, 1470/7002?
Answer: GCF of Numerators as per given numbers 28/178, 1470/7002 is
GCF of Numerators i.e. for 28,1470 is 14
LCM of denominators i.e. for 178,7002 is 623178.
Thus, GCF of Fractions is 14/623178.Finally, GCF of Fractions for 28/178, 1470/7002 is 14/623178.