If x=22x3x52 and y=22x33 then HCF[xy] = ?
x = 22x3x52
= 2x11x3x2x2x13
y = 22x33
= 2x11x3x11
HCF = 2x3x11 = 66
thank you sir.
To find the HCF (Highest Common Factor) of two numbers, we need to factorize both numbers completely and identify the common factors.
First, let's expand the expressions for x and y:
x = 22 × 3 × 52
= 2 × 2 × 3 × 5 × 5
y = 22 × 33
= 2 × 2 × 3 × 3 × 3
Now, let's find the prime factors of x and y. Prime factors are the numbers that divide a given number exactly, without leaving a remainder.
Prime factors of x:
2, 2, 3, 5, 5
Prime factors of y:
2, 2, 3, 3, 3
Next, to find the HCF, we look for the common factors in both factorizations.
Factors common to both x and y:
2, 2, 3
To find the HCF, we multiply all the common factors:
HCF[xy] = 2 × 2 × 3 = 12
Therefore, the HCF of xy is 12.