How do you find the factors of 109?

Finding the factors of a number like 109 involves determining which whole numbers can be multiplied together to produce that number. Let's break this down step by step.

Understanding Factors

Factors are integers that divide another integer without leaving a remainder. For example, if you take the number 12, its factors include 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to equal 12.

Identifying Factors of 109

To find the factors of 109, we start by checking the integers from 1 up to the square root of 109. The square root of 109 is approximately 10.44, so we will check the integers from 1 to 10.

• 1: 109 ÷ 1 = 109 (1 is a factor)
• 2: 109 ÷ 2 = 54.5 (not a factor)
• 3: 109 ÷ 3 = 36.33 (not a factor)
• 4: 109 ÷ 4 = 27.25 (not a factor)
• 5: 109 ÷ 5 = 21.8 (not a factor)
• 6: 109 ÷ 6 = 18.17 (not a factor)
• 7: 109 ÷ 7 = 15.57 (not a factor)
• 8: 109 ÷ 8 = 13.625 (not a factor)
• 9: 109 ÷ 9 = 12.11 (not a factor)
• 10: 109 ÷ 10 = 10.9 (not a factor)

Conclusion on Factors

After checking all integers up to 10, we find that the only whole numbers that divide 109 without leaving a remainder are 1 and 109 itself. This means that 109 is a prime number, as it has no other factors besides 1 and itself.

Why is This Important?

Understanding factors is crucial in various areas of mathematics, including simplifying fractions, finding least common multiples, and solving equations. Recognizing prime numbers like 109 helps in number theory and can be applied in fields such as cryptography.

In summary, the factors of 109 are simply 1 and 109, confirming its status as a prime number. If you have any more questions about factors or related concepts, feel free to ask!