Question

Express the following number as the sum of three odd prime numbers: 49. \[\]

Answer 1

Hint: We recall the even, odd, prime, and composite numbers. Since we have to write three odd numbers whose sum is 49, we write down all the odd primes below 49. We take different combinations and try to guess 3 odd primes.
\[\]

Complete step by step answer:
We know that we call a number an even number when the number is exactly divisible by 2, for example, 2,4,6,8, and so on. We call a number an odd number when the number is not exactly divisible by 2, for example, 1,3,5,7, and so on.

We know that we call a number a prime number when the number has only two factors: 1 and the number itself. We know that we call a number composite when the number has more than 2 factors.\[\]

We are asked in the question to find three odd numbers such that their sum will be 49. If the sum is going to 59, the prime numbers cannot be greater than 49. Let us write all the primes below 49. We have the primes as
\[2,3,5,7,11,13,17,19,21,23,29,31,37,43,47\]

Since we can only choose odd primes we reject the even prime 2 and we choose only from numbers
\[3,5,7,11,13,17,19,21,23,29,31,37,43,47\]

Let us choose one prime randomly as 3. Now we have to choose the other two odd primes such that their sum will be $ 49-3=6 $. We focus digits at one’s place and choose primes such that the sum of digits will return 6 in the one’ place of their sum like $ 1+5=6,7+9=16 $ . We choose 17 and 29 to have the sum of $ 17+29=46 $. Hence three odd primes are $ 3,17,29 $ whose sum is
\[3+17+29=49\]

Note:
we can also choose $ 5,7,37 $ or $ 7,11,29 $ and many more three odd primes for the solution. We should remember that we call a dividend exactly divisible when we get remainder 0 after the division and we call the divisor a factor of the dividend when the divisor exactly divides the dividend.