Recognizing divisibility  Factors and multiples  PreAlgebra  Khan Academy  Summary and Q&A
TL;DR
Determine whether 380 is divisible by 2, 3, 4, 5, 6, 9 or 10 by examining its characteristics.
Questions & Answers
Q: How can you determine if a number is divisible by 2?
To determine divisibility by 2, check if the ones digit is even. In the case of 380, since the ones digit is 0, it is divisible by 2.
Q: What is the rule for divisibility by 3?
One rule states that if the sum of the digits is divisible by 3, then the number is divisible by 3. However, since the sum of the digits of 380 (11) is not divisible by 3, it is not divisible by 3.
Q: How does divisibility by 4 work?
If a number is divisible by 4, the last two digits should be divisible by 4. In the case of 380, since 80 is divisible by 4, 380 is also divisible by 4.
Q: What is the rule for divisibility by 5?
Numbers that end with either 5 or 0 are divisible by 5. Since 380 ends with 0, it is divisible by 5.
Q: How can you determine if a number is divisible by both 2 and 3?
A number divisible by 2 and 3 must have both an even ones digit and its digit sum should be divisible by 3. Since 380 fails to satisfy the divisibility by 3 requirement, it is not divisible by both 2 and 3.
Q: Why is divisibility by 9 related to divisibility by 3?
Divisibility by 9 requires a number to be divisible by 3 at least twice. Since 380 is not divisible by 3, it is also not divisible by 9.
Q: How can you determine if a number is divisible by 10?
Numbers that end with 0 are divisible by 10. As 380 ends with 0, it is divisible by 10.
Summary & Key Takeaways

To determine divisibility by 2, the ones digit of 380 should be even, and since it is 0, 380 is divisible by 2.

Adding the digits of 380 (3 + 8 + 0) yields 11, which is not divisible by 3, so 380 is not divisible by 3.

Since 100 is divisible by 4, the remainder 80 is checked for divisibility, and since it is divisible by 4, 380 is divisible by 4.

Ending with a 0, 380 is divisible by 5.

380 is not divisible by 6 since it is not divisible by both 2 and 3.

380 is not divisible by 9 since it is not divisible by 3.

380, having a digit 0 in the ones place, is divisible by 10.