## Moderate Problems On HCF

Dear Reader,

Below are four problems based on the HCF of two or three numbers with simple steps.

**Question 1**

HCF of the numbers 2^{3} x 3^{3} x 11^{2} x 23, 2^{2} x 3 x 7^{2} x 11^{3} x 23^{2} is :

a)33396 b)34523 c)45782 d)23846

**Answer :** a)33396

**Solution:**

HCF of the numbers = the product of the lowest powers of the common factors

The prime factors common to given numbers are 2, 3, 11 and 23.

Here, the common prime factors with the lowest power are 2^{2}, 3, 11^{2} and 23

Then the product = 2^{2} x 3 x 11^{2} x 23 = 4 x 3 x 121 x 23 = 33396.

Hence the answer is 33396.

**Question 2**

HCF of the numbers 234, 390 and 8190 is :

a)234 b)390 c)78 d)117

**Answer :** c)78

**Solution:**

First express the given numbers as the product of prime numbers as follows:

i.e., 234 = 2 x 3^{2} x 13

390 = 2 x 3 x 5 x 13

8190 = 2 x 3^{2} x 5 x 7 x 13

The factors common to the three numbers are 2, 3 and 13

And the product of the common factors = 2 x 3 x 13 = 78

**Question 3**

Find the H.C.F. of 1.8, 1.05 and 3.15

a)0.15 b)0.18 c)1.8 d)1.05

**Answer :**a)0.15

**Solution:**

**Note :**" H.C.F. and L.C.M. of Decimal Fractions: In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers without decimal point, find H.C.F. or L.C.M. as the case may be. Now, in the result, mark off as many decimal places as are there in each of the given number"

Making the same number of decimal places, the given numbers are 1.80, 1.05 and 3.15 .

Without decimal places, these numbers are 180, 105 and 315.

Now, H.C.F. of 180, 105 and 315 is 15.

Then H.C.F. of 1.8, 1.05 and 3.15 is 0.15.

Hence the required answer is 0.15.

**Question 4**

Reduce 900/1890 to lowest terms.

a)20/42 b)90/189 c)10/21 d)30/63

**Answer :** c).10/21

**Solution:**

We know that "If P/Q is any fraction and X/Y is reduced fraction of P/Q as lowest terms then X = P/M and Y = Q/M where M is the HCF of P and Q"

Now, 900 = 2^{2} x 3^{2} x 5^{2}

and 1890 = 2 x 3^{3} x 5 x 7

Then the HCF of 900, 1890 = 2 x 3^{2} x 5 = 90.

And 900/90 = 10, 1890/90 = 21

Then the required answer is 10/21