What are the factors of 55?

(a) 1, 7, 55

(b) 1, 5, 11, 55

(c) 1, 7, 9, 55

(d) None of these

To determine the factors of 55, we need to identify all the whole numbers that can divide 55 without leaving a remainder. Factors are essentially the numbers that multiply together to yield the original number. Let's break this down step by step.

Finding Factors of 55

First, we can start by testing the smallest integers to see if they divide evenly into 55:

• 1: 55 ÷ 1 = 55 (1 is a factor)
• 2: 55 is odd, so it cannot be divided by 2.
• 3: The sum of the digits (5 + 5 = 10) is not divisible by 3, so 3 is not a factor.
• 4: 55 is not divisible by 4 (55 ÷ 4 = 13.75).
• 5: 55 ÷ 5 = 11 (5 is a factor)
• 6: 55 is not divisible by 6 (55 ÷ 6 = 9.1667).
• 7: 55 ÷ 7 = 7.8571 (not a factor).
• 8: 55 is not divisible by 8 (55 ÷ 8 = 6.875).
• 9: 55 is not divisible by 9 (55 ÷ 9 = 6.1111).
• 10: 55 is not divisible by 10 (55 ÷ 10 = 5.5).
• 11: 55 ÷ 11 = 5 (11 is a factor)
• 55: 55 ÷ 55 = 1 (55 is a factor)

Summary of Factors

From our calculations, we find that the factors of 55 are:

• 1
• 5
• 11
• 55

Now, let’s compare these factors with the options provided:

• (a) 1, 7, 55 - Incorrect (7 is not a factor)
• (b) 1, 5, 11, 55 - Correct (all are factors)
• (c) 1, 7, 9, 55 - Incorrect (7 and 9 are not factors)
• (d) None of these - Incorrect (option b is correct)

Final Answer

The correct choice is (b) 1, 5, 11, 55. Understanding factors is crucial in various areas of mathematics, including simplifying fractions, finding common denominators, and solving equations. If you have any more questions about factors or related concepts, feel free to ask!