19. What are the factors of 158?

A. 1, 2, 79, 158
B. [tex]$1, 2, 58, 100, 158$[/tex]
C. [tex]$1, 5, 8, 10, 79, 158$[/tex]
D. [tex]$2, 79, 158$[/tex]



Answer :

To determine the factors of 158, we need to find all integers that divide 158 without leaving a remainder. Here’s a step-by-step approach to identifying the factors:

1. Start with the smallest integer, which is 1:
- Since any number divided by 1 is the number itself, 1 is a factor of 158.

2. Check the next integer, 2:
- 158 is an even number, and all even numbers are divisible by 2.
- 158 ÷ 2 = 79, thus 2 and 79 are both factors of 158.

3. Check subsequent integers up to the square root of 158:
- Beyond 2, we continue checking integers (3, 4, 5, etc.) until approximately the square root of 158. The square root of 158 is slightly less than 13.
- For each of these integers, we see if 158 can be divided evenly (without remainder).

4. Direct verification:
- For numbers like 3, 4, 5, and up to 12, directly checking reveals that none of these numbers divide 158 evenly.

5. Always include the number itself:
- Since any number is divisible by itself, 158 is a factor of 158.

Synthesizing the results, we find that the factors of 158 are:
1, 2, 79, and 158.

From the given options:

(A) 1, 2, 79, 158

(B) 1, 2, 58, 100, 158

(C) 1, 5, 8, 10, 79, 158

(D) 2, 79, 158

The correct set of factors matches option (A): 1, 2, 79, 158.

Therefore, the correct answer is:
(A) 1, 2, 79, 158.