What are the factors of 65?
Understand the Problem
The question is asking for the factors of the number 65, which are the integers that can be multiplied together to produce 65. We will identify all positive integers that divide 65 without leaving a remainder.
Answer
1, 5, 13, 65
Answer for screen readers
The factors of 65 are 1, 5, 13, and 65
Steps to Solve
- Identify pairs of numbers that multiply to 65
Since we need to find the factors, let's start by dividing 65 by different numbers to see which pairs multiply to 65.
- Check for divisibility starting from 1 upwards
First, check if 1 is a factor: $65 \div 1 = 65$, so (1, 65) is a pair.
Next, check 2: 65 is not divisible by 2 since it's an odd number.
Try 3: $65 \div 3 \approx 21.67$, so 3 is not a factor.
Then check 4: since 65 is odd, it cannot be divisible by an even number like 4.
Check 5: $65 \div 5 = 13$, so (5, 13) is a pair.
Next, check 6, 7, 8, 9, 10, 11, and 12: 65 is not divisible evenly by any of these.
Then check 13: We already checked above that 65 divided by 13 gives us 5, so (13, 5) is a repeated pair.
- List all unique factor pairs
From our checks, the pairs are (1, 65) and (5, 13).
So the factors of 65 are: 1, 5, 13, and 65.
The factors of 65 are 1, 5, 13, and 65
More Information
65 is a semiprime number because it is the product of two prime numbers, 5 and 13.
Tips
A common mistake is to forget checking for factors beyond the square root of the number. Always remember to go through all integers up to the number itself.
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