The HCF of 2 no. Is 1/28 of their LCM.The sum of the HCF and the LCM is 116.If one of the no. Is 16 , find the other.
H = (1/28)L
L = 28H
L + H = 116
28H + H = 116
29H = 116
H = 4
then L = 112
one number is 16
let the other number be 4x
then :
16 = 4*4
4x = 4*x
16x = 112
x = 7
and 4x= 28
The other number is 28
check:
16 = 2*2*2*2
28=2*2*7
LCF = 2*2 = 4
HCM = 2*2*2*2*7 = 112
is 4 equal to 1/28 of 112 ? yes
is 4+ 112 = 116 ? , YES
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To find the other number, let's first calculate the HCF (Highest Common Factor) and LCM (Least Common Multiple).
Given that the HCF of two numbers is 1/28 of their LCM, we can express this mathematically as:
HCF = (1/28) * LCM
We also know that the sum of the HCF and LCM is 116:
HCF + LCM = 116
Let's substitute the value of HCF from the first equation into the second equation:
(1/28) * LCM + LCM = 116
To simplify the equation, let's multiply everything by 28 to remove the fraction:
LCM + 28 * LCM = 116 * 28
29 * LCM = 3248
Now, divide both sides of the equation by 29:
LCM = 3248 / 29
LCM ≈ 112
We can now substitute the LCM value back into the first equation to find the HCF:
HCF = (1/28) * 112
HCF ≈ 4
Finally, since one of the numbers is given as 16, we can use the relationship between the HCF and the given number to find the other number:
HCF = GCD(a, b)
where GCD is the Greatest Common Divisor function, and (a, b) are the two numbers.
Since the HCF is 4, we can express this mathematically as:
4 = GCD(16, b)
To find b, we need to find the factors of 16 that have 4 as the GCD:
The factors of 16 are 1, 2, 4, 8, and 16.
Out of these, only 4 is the common factor with 4.
Therefore, the other number is 4.
So, the other number is 4.