Question

Express $7429$ as a product of its prime factors.

Answer 1

Hint: In this question, we need to find express $7429$ as the product of its prime factors. Here, we will determine the factors of $7429$ and then we will determine the prime factors of $7429$, using the method of prime factorization.

Complete step by step answer:
Here, we need to find the prime factors of $7429$ using prime factorization.We know that $7429$ is a composite number. Therefore, the possible factors of $210$ are: $7429 \times 1$, $437 \times 17$, $391 \times 19$, $323 \times 23$.Prime factorization is a method of finding prime numbers which multiply to make the original number. A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers.

In prime factorization, we start dividing the number by the first prime number $2$ and continue to divide by $2$ until we get a decimal or remainder. Then divide by $3,5,7,....$etc. until we get the remainder $1$ with the factors as prime numbers. Then write the numbers as a product of prime numbers. Thus, prime factorization of $7429$ is,
$7429 = 17 \times 19 \times 23$
This can be also written in exponential form. But as all the prime factors appear only once in the prime factorisation of $7429$.

Hence, the $7429$ can be expressed as a product of its prime factors as $17 \times 19 \times 23$.

Note: In this question it is important to note here that a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $1$ and itself. However, the prime factorization is also known as prime decomposition. And, the prime factorization of the prime number is the number itself and $1$. Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers.