To find all the factors of 375, you need to determine all the integers that can divide 375 without leaving a remainder. Here's a detailed, step-by-step explanation:
1. Start with the smallest integer, 1:
- Since 1 divides every number, 1 is a factor of 375.
2. Consider the next integer, 2:
- 375 is an odd number, which means it is not divisible by 2. So, 2 is not a factor of 375.
3. Proceed to the next integer, 3:
- Check if 375 is divisible by 3.
- When you divide 375 by 3, the result is 125 with no remainder, so 3 is a factor.
4. Continue with integers up to the square root of 375 (~19.4) and check divisibility:
- For 4: 375 is not divisible by 4.
- For 5: 375 divided by 5 equals 75, so 5 is a factor.
- For 6 through 14: 375 is not divisible by these numbers.
- For 15: 375 divided by 15 equals 25, so 15 is a factor.
- For 16 through 24: 375 is not divisible by these numbers.
- For 25: 375 divided by 25 equals 15, so 25 is a factor.
- For 26 through 74: 375 is not divisible by these numbers.
- For 75: 375 divided by 75 equals 5, so 75 is a factor.
- For 76 through 124: 375 is not divisible by these numbers.
- For 125: 375 divided by 125 equals 3, so 125 is a factor.
- For 126 through 374: 375 is not divisible by these numbers.
- For 375: 375 divided by 375 equals 1, so 375 is a factor.
5. Collect all pairs:
- As you identify each factor and its corresponding pair from dividing 375, you gather these numbers: 1, 3, 5, 15, 25, 75, 125, and 375.
6. List all factors in ascending order:
- To clearly list all factors, arrange them in ascending order.
Hence, the complete list of factors of 375 is:
[tex]\[1, 3, 5, 15, 25, 75, 125, 375\][/tex]
