Question

What are two numbers between $ 60 $ and $ 70 $ that are products of two prime numbers?

Answer 1

Hint: First of all list numbers between the given range and then find the factors of the numbers and then identify the two numbers which are the product of two prime numbers. Prime numbers can be defined as numbers which have only two factors: the number itself and the number one.

Complete step-by-step answer:
List out all the prime and composite numbers between the given range of the numbers $ 60 $ and $ 70 $
Prime numbers: $ 61,67 $
Composite numbers: $ 62,63,64,65,66,68,69,70 $
Now find the factors for all the composite numbers –
 $
  62 = 1,2,31 \\
  63 = 1,3,3,7 \\
  64 = 1,8,8 \\
  65 = 1,5,13 \\
  66 = 1,6,11 \\
  68 = 1,4,17 \\
  69 = 1,3,23 \\
  $
From observing the above factors of the terms-
We can find that there are two numbers in the given range which can be split in the numbers which are prime numbers and when multiplied together gives the original number.
 $ 65 = 5 \times 13 $ and $ 69 = 3 \times 23 $
Hence, the two numbers between $ 60 $ and $ 70 $ that are products of two prime numbers are $ 65 $ and $ 69 $
So, the correct answer is “ $ 65 $ and $ 69 $ ”.

Note: Do not get confused between the prime and the composite numbers. Prime numbers are not divisible by the number itself and not with any other number than that. Composite numbers have more than two factors. Be good in multiples and division to get the factors of any given number. Factorization can be done by prime factorization, long division or factor-tree method.