Solved on Feb 24, 2024
Determine if the number is divisible by , and/or . If not, answer "None".
STEP 1
Assumptions
1. We need to determine the divisibility of the number 97 by 2, 3, 4, 5, 6, 8, 9, and 10.
2. A number is divisible by 2 if it is even, which means its last digit is 0, 2, 4, 6, or 8.
3. A number is divisible by 3 if the sum of its digits is divisible by 3.
4. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
5. A number is divisible by 5 if its last digit is 0 or 5.
6. A number is divisible by 6 if it is divisible by both 2 and 3.
7. A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
8. A number is divisible by 9 if the sum of its digits is divisible by 9.
9. A number is divisible by 10 if its last digit is 0.
STEP 2
Check for divisibility by 2.
Since the last digit of 97 is not 0, 2, 4, 6, or 8, it is not divisible by 2.
STEP 3
Check for divisibility by 3.
The sum of the digits of 97 is , which is not divisible by 3. Therefore, 97 is not divisible by 3.
STEP 4
Check for divisibility by 4.
The last two digits of 97 are 97 itself, and since 97 is not divisible by 4, the number 97 is not divisible by 4.
STEP 5
Check for divisibility by 5.
Since the last digit of 97 is not 0 or 5, it is not divisible by 5.
STEP 6
Check for divisibility by 6.
Since 97 is not divisible by 2 or 3, it cannot be divisible by 6.
STEP 7
Check for divisibility by 8.
For a number to be divisible by 8, the number formed by its last three digits must be divisible by 8. Since 97 is less than 100, we only consider the number itself, which is not divisible by 8.
STEP 8
Check for divisibility by 9.
The sum of the digits of 97 is 16, which is not divisible by 9. Therefore, 97 is not divisible by 9.
STEP 9
Check for divisibility by 10.
Since the last digit of 97 is not 0, it is not divisible by 10.
STEP 10
Conclusion
After checking all the given divisors, we find that 97 is not divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Therefore, the answer is "None".
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