Question

if p= 2(4)(6)....(20) and Q= 1(3)5.....19 hcf of P and Q is

Answer 1

Since P = 2(4)(6)....(20) and Q= 1(3)(5)(7).....(19)

We have to find the HCF of P and Q.

"The H.C.F. of the numbers is the product of the common prime factors."

Since in P, there are prime numbers 2,3,5,7.

In Q, there are no factors of 2.

So, the HCF of P and Q will surely not have 2, therefore, it will have 3,5 and 7.

In P, 3's comes from 6,12,18.

6 =$3 \times 2$, 12= $3 \times 2 \times 2$ , $18 = 2 \times 3 \times 3$

Therefore, $3^4$ is the greatest power of 3 that is a factor of P.

In Q, 3's comes from 3,9 and 15

3 =$3 \times 1$, 9= $3 \times 3$ , $15 = 3 \times 5$

Therefore,  $3^4$ is also a factor of Q.

Similarly $5^2$ is the greatest power of 5 in P and Q.

And 7 is the greatest power in P and Q.

So, HCF of P and Q = $3^4 \times 5^2 \times 7$

= 14175

Therefore, HCF of P and Q is $3^4 \times 5^2 \times 7$ or 14175.

Answer 2

In case p= 2 (4) (6).... (20) and Q = 1 (3) 5 ..... 19 hcf of P and Q is 23.

Most noteworthy Common Factor(HCF) of at least two numbers is the best number which separates every one of them precisely.

Most prominent Common Measure (GCM) and Greatest Common Divisor (GCD) are alternate terms used to allude HCF.