GCF of 160/224, 670/312, 284/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 160/224, 670/312, 284/419 i.e 2/3660384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 160/224, 670/312, 284/419.
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 160/224,670/312,284/419?
Given fractions are 160/224,670/312,284/419
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 160/224,670/312,284/419, numerators are 160,670,284
Denominators are 224,312,419
The GCF of 160,670,284 is 2 .
LCM of 224,312,419 is 3660384.
The greatest common factor of 160/224,670/312,284/419 = [GCF of 160,670,284]/[LCM of 224,312,419]= 2/3660384
Therefore, the GCF of 160/224,670/312,284/419 is 2/3660384.
To find the highest common factor of 160,670,284, we have to find the factors of both numbers and list the highest common factor.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The factors of 284 are 1, 2, 4, 71, 142, 284
The HCF of 160,670,284 is 2.
Lets's calculate GCF of 160,670,284
| 2 | 160, 670, 284 |
| 80, 335, 142 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 160,670,284 By Matching Biggest Common Factor Method
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Now, list down the factors of 284
:1,2,4,71,142,284
Greatest Common Factor
We found the factors 160,670,284 . The biggest common factor number is the GCF number.
So the greatest common factor 160,670,284 is 2.
Lets's calculate LCM of 224,312,419
| 2 | 224, 312, 419 |
| 2 | 112, 156, 419 |
| 2 | 56, 78, 419 |
| 28, 39, 419 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 28 x 39 x 419 = 3660384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3660384
Therefore, the GCF of Fractions 160/224,670/312,284/419 is 2/3660384
Least Common Multiple of 224,312,419 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 224,312,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,312,419) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(224,312,419) x common factors =1 x 8 = 8
LCM(224,312,419) = ( 224 × 312 × 419 ) / 8
LCM(224,312,419) = 29283072 / 8
LCM(224,312,419) = 3660384
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 160/224, 670/312, 284/419
1. What is the HCF of 160,670,284?
The HCF of 160,670,284 is 2
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 160/224, 670/312, 284/419?
Answer: GCF of Numerators as per given numbers 160/224, 670/312, 284/419 is
GCF of Numerators i.e. for 160,670,284 is 2
LCM of denominators i.e. for 224,312,419 is 3660384.
Thus, GCF of Fractions is 2/3660384.Finally, GCF of Fractions for 160/224, 670/312, 284/419 is 2/3660384.