Question

How do you write 720 as a product of its prime factors?

Answer 1

Hint: Here, we will use the prime factorization method to find the prime factors of the given number 720. Then we will multiply all the obtained factors to express the given number as a product of its prime factors.

Complete step-by-step answer:
In this question, we are required to express the given number as a product of its prime factors.
First of all, prime factors are those factors which are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself.
Now, in order to express the given number as a product of its prime factors, we are required to do the prime factorization of the given number.
Now, factorization is a method of writing an original number as the product of its various factors.
Hence, prime factorization is a method in which we write the original number as the product of various prime numbers.
We will now do prime factorization of 720.
We can see that 720 is an even number, so we will divide it by the least prime number 2. Therefore, we get
\[720 \div 2 = 360\]
As 360 is also an even number, so we will again divide by 2.
\[360 \div 2 = 180\]
Dividing 180 by 2, we get
\[180 \div 2 = 90\]
Dividing 90 by 2, we get
\[90 \div 2 = 45\]
Now dividing 45 by the next least prime number 3, we get
\[45 \div 3 = 15\]
Dividing 15 by 3, we get
\[15 \div 3 = 5\]
As we have obtained the quotient as a prime number, so we will not divide the number further.
Hence, 720 can be written as:
\[720 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5\]

Hence, we have expressed the given number as a product of its prime factors.

Note: Here the given number is a composite number. A number is said to be a composite number if it is completely divisible by 2. We can express any composite number as a product number of prime factors. The smallest prime number is 2 and there are 25 prime numbers between 1 to 100. 1 is neither prime nor composite soi t cannot be expressed as a product of prime factors.