Question

b) Written as product of their prime factors
N= 2^p * 5^q * 7^r
and 500= 2^2 * 5^3
The highest common factor of N and 500
is 2²x5^2? The lowest common multiple of
N and 500 is
2²x5²x7.
Find p, q and r

Answer 1

Given : Written as product of their prime factors

N= 2^p * 5^q * 7^r  and 500= 2^2 * 5^3

The highest common factor of N and 500  is 2²x5^2? The lowest common multiple of  N and 500 is  2²x5²x7.

To Find : p, q and r

Solution:

N= 2^p * 5^q * 7^r

500= 2² * 5³

highest common factor of N and 500  is 2²x5²

p ≥ 2

q = 2

r ≥ 0

The lowest common multiple of  N and 500 is  2²x5²x7.

HCF x LCM = N * 500

=> 2²x5²  x 2²x5²x7 = 2^p * 5^q * 7^r  x 2² * 5³

=>  2²x5x7 = 2^p * 5^q * 7^r

p = 2

q = 1  but q = 2 as per HCF

r = 1

There is mistake in data

As LCM should have 5^3 atleast as 500 has 5^2

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Answer 2

Answer:

p 3 q 2 r

Step-by-step explanation: