Factorize the Expression: 37a + 6b Step-by-Step

Let's factor the given expression:

$37a+6b$We will do this by extracting the greatest common factor, both for numbers and letters,

We will address numbers and letters separately, remembering that a common factor is a factor (multiplier) that is common to all terms in the expression,

Let's start with the numbers:

Note that for the two numerical coefficients of the terms in the expression, namely the numbers 6 and 37, there is no single factor that is common to both, while the factors of the number 6 are the numbers 2 and 3 or 6 and 1, the number 37 is a prime number and therefore its only factors are 37 and 1, meaning - there is no factor that is common to these two numbers, therefore - the number 1 (which is essentially the 0 power of any number - except 0) will be considered instead of the common factor for numbers.

For the letters:

There are two terms:
$a,\hspace{4pt}b$It's easy to see that there is no factor common to these two terms,$a$therefore there is no algebraic expression for letters that could be a common factor, meaning - the number 1 (which is essentially the 0 power of any number - except 0) will be considered instead of the common factor for letters.

Therefore we conclude:

This expression cannot be factored by extracting a common factor (or in any other way)

Therefore the correct answer is answer D.