Question

The product of all the prime numbers less than $20$ is closest to which of the following powers of $10$
(A) ${10^9}$
(B) ${10^8}$
(C) ${10^7}$
(D) ${10^6}$
(E) ${10^5}$

Answer 1

Hint: A prime number (or a prime) is a natural number greater than $1$ that is not a product of two smaller natural numbers. A natural number greater than $1$ that is not prime is called a composite number.

Let’s explain with example:
$5$ is prime because the only way of writing it is as a product. $1 \times 5$ or $5 \times 1$ involve $5$ itself.
And let’s take another example.
$4$ is a composite number because it is a product $2 \times 2$ in which both numbers are smaller than $4.$
Prime numbers are the central in number theory because the fundamental theorem number greater than $1$ is either a prime itself or can be factorized as a product of primers that is unique up to their order.
Some other example of prime number are:
$3$ is a prime it can be written as $3 \times 1$ or $1 \times 3$
$11$ is a prime it can be written as $1 \times 11$ or $11 \times 1$

Complete Step by Step Solution:
Given that we have to find the product of prime numbers less than $20.$
So, we need to determine the product of.
$2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19$
Now, let’s group some of the number to get power of $10.$
$5 \times 19$ is about to form $100 = {10^2}$
So, we are left with
$2 \times 3 \times 7 \times 11 \times 13 \times 17$
And $7 \times 13$ is about form $100 = {10^2}$
So, we are left with
$2 \times 3 \times 11 \times 17$
$2 \times 3 \times 17$ is about to form $100 = {10^2}$
About $10 = {10^1}.$
Now,
The product of all the prime numbers less than $20$ is.
${10^2} \times {10^2} \times {10^2} \times {10^1} = {10^7}$

Hence, the correct answer is option (C).

Note: Prime numbers do not include $1$ so remember not to add $1$ in the prime number list. The product of prime numbers includes $1$ because the factors of prime numbers are $1$ and the number itself.