Discover All the Factors of 290: Step-by-Step Guide

To solve this problem, we'll follow these steps:

• Step 1: Perform prime factorization on 290.
• Step 2: Determine all prime factors.
• Step 3: Compare prime factors to the given choices.

Now, let's work through each step:

Step 1: Start by dividing 290 by the smallest prime number, which is 2:
$290 \div 2 = 145$
So, 2 is a prime factor.

Step 2: Next, divide 145 by the next smallest prime number, which is 5:
$145 \div 5 = 29$
Both 5 and 29 are prime numbers.

Since 29 is itself a prime number, it cannot be divided further. Therefore, the complete prime factorization of 290 is $2 \times 5 \times 29$.

Step 3: Compare these results with the answer choices provided:

• Choice 1: $3,2,26$ - This is incorrect because 290 is not divisible by 3 or 26.
• Choice 2: $5,2,29$ - This is correct since all these are prime factors of 290.
• Choice 3: $1,5,7$ - This is incorrect. 7 is not a factor, and 1 is not a prime number.
• Choice 4: $3,29,2$ - This is incorrect because 290 is not divisible by 3.

Therefore, the correct answer is $5,2,29$.