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.
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.
