Question

How do you express $ 3080 $ as a product of prime factors?

Answer 1

Hint: Prime numbers are the whole number greater than 1 which cannot be made by multiplying other whole numbers such as $ 2,3,5,.... $ are prime numbers. Remember number one is neither prime nor composite. Here we will find the prime factors of the given number by deducing the number into multiples.

Complete step by step solution:
Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $

Start dividing the given number with the least prime number $ 2 $ , if it is further not divided then start dividing with next least prime number that is $ 3 $ and so on...
So, the factors of the given number can be expressed as –
 $ \Rightarrow 3080 = 308 \times 10 $
We can observe in the above equation, that the factors on the right-hand side of the equation are the composite numbers. Deduce them in the form of a product of prime.
 $
 \Rightarrow 3080 = 154 \times 2 \times 2 \times 5 \\
 \Rightarrow 3080 = 2 \times 77 \times 2 \times 2 \times 5 \\
 \Rightarrow 3080 = 2 \times 7 \times 11 \times 2 \times 2 \times 5 \\
  $
Arranging the multiples on the right-hand side of the equation.
 $ \Rightarrow 3080 = 2 \times 2 \times 2 \times 5 \times 7 \times 11 $
This is the required solution.

Note: Remember that the factors of the given number can be calculated by using the long division method or by factor tree method. To find the factors you should convert the given number in prime factors. Know the difference between the prime and composite numbers. You should be very good in multiples. As, ultimately your answer depends on the multiplication of the numbers. Remember multiplies of the number at least till for the accurate and efficient solution.