Question

Express the following number as a product of its prime factor: 7429
$\begin{align}
  & a)11\times 19\times 23 \\
 & b)17\times 19\times 23 \\
 & c)17\times 23\times 23 \\
 & d)17\times 19\times 29 \\
\end{align}$

Answer 1

Hint: First we will try to find the first factor of the number 7429 by using the test of divisibility. Similarly to the obtained factors we will again factorize it in a similar manner till we arrive at prime factorization.

Complete step-by-step answer:
Now let us first understand the concept of factors.
Now consider any two numbers let us say 2 and 3.
Now we know that 2 × 3 = 6.
Hence 2 and 3 are called factors of 6.
Now prime factors are the factors which are prime numbers. Hence 2 and 3 are prime factors of 6.
Now to express the number in a product of prime factors means to express it as multiplication of prime numbers.
Now we have 2 and 3 as prime numbers hence 6 = 2 × 3 is prime factorization of 6.
Now note that any number can be written as a product of prime factors.
For example if we have 8 then 8 can be written as 8 = 2 × 2 × 2.
Now let us consider the given number which is 7429.
Now the first number that divides 7429 is 17.
Hence we have 7429 = 17 × 437.
Now 17 is a prime number.
Hence consider the number 437.
The first number that divides 437 is 19.
Hence we have 437 = 19 × 23.
Here 19 and 23 are prime numbers.
Hence we can say that 4729 = 17 × 437 = 17 × 19 × 23.
Hence we have 4729 = 17 × 19 × 23
Hence option b is the correct option.

So, the correct answer is “Option b”.

Note: Now the prime numbers are the numbers which can be only divided with 1 and the number itself. Hence the prime factorization of a prime number is not possible. Hence we stop factorization when we arrive at a prime number.