Question

The product of divisors of 343 is.
A.${7^{\dfrac{3}{2}}}$
B.${7^2}$
C.\[{7^3}\]
D.\[{7^6}\]

Answer 1

Hint: We have to find the product of divisors of 343. We will first find the divisors of the 343. We will do prime factorization of the number 343 to write all the divisors. Then, write the product of the divisors to get the required answer.

Complete step-by-step answer:
First of all, we will calculate the divisors of the given number.
We will write the prime-factorization of numbers to determine the product of divisors for the number 343.
We will first divide 343 by the smallest prime number that divides it completely, hence, divide by 7. Then, write the quotient in the next line and this is our new number. Again, divide the number by the smallest prime that divides is completely and repeat the process till we get quotient as 1.

7	343
7	49
7	7
	1

 Therefore, the 343 is also equal to $7 \times 7 \times 7$ which can also be written as \[{7^3}\]
Thus, the product of divisors of 343 is \[{7^3}\]
Hence, option C is correct.

Note: The divisor is the number which divides the given number completely. Here, the divisors of 343 are 1,49 and 7. The product of divisors is $1 \times 49 \times 7 = {7^3}$