Question

determine the values of p and q so that the prime factors of 2520 are in the form of 2 raise to power 3 X 3 raise to power p X q X 7

Answer 1

2 and 5 is the value of p and q respectively.

Given:

$2^{3} \times 3^{p} \times q \times 7$ is the prime factor of 2520.  

To find:

Value of p and q

Solution:

To find the prime factor of the number 2520, we use the long division method in which the lowest prime factor other than 1 is used, in this case it is 2 after that we use variety of prime number odd or even, in the case of 2520 the factors are $2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7=2^{3} \times 3^{2} \times 5 \times 7.$

Now the question is written in form of 2 raise to power $3 \times 3$ raise to power$p \times q \times 7$, which means the first factor that is $2^{3}$  is same the next factor $3^{p}$ , here p = 2, and then next is q = 5.

Therefore, the value of p, q = 2, 5 respectively.  

Answer 2

Answer: P =2 AND Q=5

2*2*2*3*3*5*7 = 2520 ( ANSWER )

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