Answer :
To determine if 36,078,742 is divisible by the numbers 2, 3, 4, 5, 6, 7, 9, 10, and 11, we'll go through each one separately and explain how divisibility works for each:
1. Divisibility by 2:
- A number is divisible by 2 if its last digit is even.
- The last digit of 36,078,742 is 2, which is even, so it is divisible by 2.
2. Divisibility by 3:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Calculate the sum: 3 + 6 + 0 + 7 + 8 + 7 + 4 + 2 = 37.
- 37 is not divisible by 3, so 36,078,742 is not divisible by 3.
3. Divisibility by 4:
- A number is divisible by 4 if the last two digits form a number that is divisible by 4.
- The last two digits are 42.
- 42 is not divisible by 4, so 36,078,742 is not divisible by 4.
4. Divisibility by 5:
- A number is divisible by 5 if it ends in 0 or 5.
- The last digit is 2, so it is not divisible by 5.
5. Divisibility by 6:
- A number is divisible by 6 if it is divisible by both 2 and 3.
- We found it divisible by 2, but not by 3, so it is not divisible by 6.
6. Divisibility by 7:
- To check, apply the divisibility rule for 7, or verify through division.
- 36,078,742 is divisible by 7, as it divides evenly.
7. Divisibility by 9:
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- The sum is 37, which is not divisible by 9.
- So, 36,078,742 is not divisible by 9.
8. Divisibility by 10:
- A number is divisible by 10 if it ends in 0.
- The last digit is 2, so it is not divisible by 10.
9. Divisibility by 11:
- A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is a multiple of 11.
- Odd positions (1, 3, 5, 7): 3 + 0 + 8 + 4 = 15
- Even positions (2, 4, 6, 8): 6 + 7 + 7 + 2 = 22
- Difference = 22 - 15 = 7, which is not a multiple of 11.
- So, 36,078,742 is not divisible by 11.
In summary:
- 36,078,742 is divisible by 2 and 7.
- It is not divisible by 3, 4, 5, 6, 9, 10, or 11.
1. Divisibility by 2:
- A number is divisible by 2 if its last digit is even.
- The last digit of 36,078,742 is 2, which is even, so it is divisible by 2.
2. Divisibility by 3:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Calculate the sum: 3 + 6 + 0 + 7 + 8 + 7 + 4 + 2 = 37.
- 37 is not divisible by 3, so 36,078,742 is not divisible by 3.
3. Divisibility by 4:
- A number is divisible by 4 if the last two digits form a number that is divisible by 4.
- The last two digits are 42.
- 42 is not divisible by 4, so 36,078,742 is not divisible by 4.
4. Divisibility by 5:
- A number is divisible by 5 if it ends in 0 or 5.
- The last digit is 2, so it is not divisible by 5.
5. Divisibility by 6:
- A number is divisible by 6 if it is divisible by both 2 and 3.
- We found it divisible by 2, but not by 3, so it is not divisible by 6.
6. Divisibility by 7:
- To check, apply the divisibility rule for 7, or verify through division.
- 36,078,742 is divisible by 7, as it divides evenly.
7. Divisibility by 9:
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- The sum is 37, which is not divisible by 9.
- So, 36,078,742 is not divisible by 9.
8. Divisibility by 10:
- A number is divisible by 10 if it ends in 0.
- The last digit is 2, so it is not divisible by 10.
9. Divisibility by 11:
- A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is a multiple of 11.
- Odd positions (1, 3, 5, 7): 3 + 0 + 8 + 4 = 15
- Even positions (2, 4, 6, 8): 6 + 7 + 7 + 2 = 22
- Difference = 22 - 15 = 7, which is not a multiple of 11.
- So, 36,078,742 is not divisible by 11.
In summary:
- 36,078,742 is divisible by 2 and 7.
- It is not divisible by 3, 4, 5, 6, 9, 10, or 11.
