Question

Express the following as a product of prime factors:
441

Answer 1

Hint: Try to find the factors of the given number. Distinguish them as prime numbers or not. If all are prime numbers, then express the given number as the product of all of them to get the required result.

Complete step by step answer:
Prime number: we know a prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers.
Prime factorization: For the prime factorization of a number we have to multiply only the prime numbers together to get the original number.
Now considering the number 441,
441 can be expressed as
$441=3\times 3\times 7\times 7$
From the above, we can conclude that the prime factors of 441 are 3 and 7 as both 3 and 7 are prime numbers.
This is the required solution of the given question.

Note: 441 can also be expressed as the product of two square numbers i.e. 9 and 49. So 441 is itself a square number, whose square root is $\sqrt{441}=\sqrt{9\times 49}=\sqrt{3\times 3\times 7\times 7}=3\times 7=21$. One major application of prime factorization is to find the greatest common factor. If two numbers are given, we have to express them as the product of prime factors. From there we can choose the greatest common factor of both the numbers as the common prime factors.