Common Factors:
Common factors are the numbers that divide two or more numbers without leaving a remainder. In other words, they are the numbers that are factors of two or more given numbers.

Common Multiples:
Common multiples are the numbers that are multiples of two or more given numbers. In other words, they are the numbers that can be divided evenly by two or more given numbers.

Common Factors of 23 and 25:
To find the common factors of 23 and 25, we need to determine the factors of each number and then identify the numbers that are common to both sets of factors.

Factors of 23:
The factors of 23 are 1 and 23 itself. Since 23 is a prime number, it only has two factors.

Factors of 25:
The factors of 25 are 1, 5, and 25.

Common Factors of 23 and 25:
From the factors listed above, we can see that the only common factor of 23 and 25 is 1.

Explanation:
- Common factors are the numbers that divide two or more numbers without leaving a remainder.
- Common multiples are the numbers that are multiples of two or more given numbers.
- To find the common factors of 23 and 25, we need to determine the factors of each number.
- The factors of 23 are 1 and 23 itself.
- The factors of 25 are 1, 5, and 25.
- The only number that is common to both sets of factors is 1.
- Therefore, the common factor of 23 and 25 is 1.

Summary:
The common factor of 23 and 25 is 1. Common factors are the numbers that divide two or more numbers without leaving a remainder, while common multiples are the numbers that are multiples of two or more given numbers. In this case, the only number that divides both 23 and 25 without leaving a remainder is 1, making it the common factor.

1 is the only common factor 23 and 25