GCF of 224/40, 320/169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 224/40, 320/169 i.e 32/6760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/40, 320/169.
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 224/40,320/169?
Given fractions are 224/40,320/169
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 224/40,320/169, numerators are 224,320
Denominators are 40,169
The GCF of 224,320 is 32 .
LCM of 40,169 is 6760.
The greatest common factor of 224/40,320/169 = [GCF of 224,320]/[LCM of 40,169]= 32/6760
Therefore, the GCF of 224/40,320/169 is 32/6760.
To find the highest common factor of 224,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 224,320 is 32.
Lets's calculate GCF of 224,320
| 2 | 224, 320 |
| 2 | 112, 160 |
| 2 | 56, 80 |
| 2 | 28, 40 |
| 2 | 14, 20 |
| 7, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 224,320 By Matching Biggest Common Factor Method
Now, list down the factors of 224
:1,2,4,7,8,14,16,28,32,56,112,224
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 224,320 . The biggest common factor number is the GCF number.
So the greatest common factor 224,320 is 32.
Lets's calculate LCM of 40,169
Given numbers has no common factors except 1. So, there LCM is their product i.e 6760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/6760
Therefore, the GCF of Fractions 224/40,320/169 is 32/6760
Least Common Multiple of 40,169 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 40,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,169) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(40,169) x common factors =1 x 1 = 1
LCM(40,169) = ( 40 × 169 ) / 1
LCM(40,169) = 6760 / 1
LCM(40,169) = 6760
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FAQs on GCF of Fractions of 224/40, 320/169
1. What is the HCF of 224,320?
The HCF of 224,320 is 32
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 224/40, 320/169?
Answer: GCF of Numerators as per given numbers 224/40, 320/169 is
GCF of Numerators i.e. for 224,320 is 32
LCM of denominators i.e. for 40,169 is 6760.
Thus, GCF of Fractions is 32/6760.Finally, GCF of Fractions for 224/40, 320/169 is 32/6760.