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Perform the divisibility test of a number by 1 to 15 for
Solution:
Consider the given number above
Without using a calculator, we can perform the divisibility test by using divisibility rules.
Divisibility by 1:
All numbers are divisible by 1 because 1 is a universal factor. Any number divided by 1 is always the same number.
Divisibility by 2:
Since the given number is an odd number, then it is not divisible by 2. All even numbers are divisible by 2.
Divisibility by 3:
To test a given number, add all the digits of a given number as follows
Since 6 is a multiple of 3, then the given number is divisible by 3.
Divisibility by 4:
Consider the given number
Since the last two digits of a given number is an odd number, then the given number is not divisible by 4. The multiples of 4 are all even numbers.
Divisibility by 5:
Since the last digit of a given number is 5, then the given number is divisible by 5. A number that ends with 5 or 0 is divisible by 5.
Divisibility by 6:
Since the given number is an odd number, then it is not divisible by 6. If an even number that is divisible by 3, then it is divisible by 6.
Divisibility by 7:
To test a given number, double the last digit and then subtract it to the rest of the digits as follows
Since the result of this process is 0, then the given number is divisible by 7. If the result of the process is a multiple of 7 or 0, then the given number is divisible by 7.
Divisibility by 8:
Consider the given number
Since the last three digits of a given number is an odd number, then the given number is not divisible by 8. The multiples of 8 are all even numbers.
Divisibility by 9:
To test a given number, add all the digits of a given number as follows
Since 6 is not a multiple of 9, then the given number is not divisible by 9.
Divisibility by 10:
Since the last digit of a given number ends with 5, then the given number is not divisible by 10. A number that ends with 0 is divisible by 10.
Divisibility by 11:
To test a given number, create two groups of the sum of alternating digits and then get their difference as follows
Since -1 is not a multiple of 11, then the given number is not divisible by 11.
Divisibility by 12:
Since the given number is divisible by 3 only and not divisible by 4 because it is an odd number, then the given number is not divisible by 12.
Divisibility by 13:
To test a given number, multiply the last digit by 4 and then add it to the rest of the digits as follows
Since 39 is a multiple of 13, then the given number is divisible by 13.
Divisibility by 14:
Although the given number is divisible by 7 but it is not divisible by 2 because it is an odd number. Because of this, the given number is not divisible by 14.
Divisibility by 15:
Since the given number is both divisible by 3 and 5, then it is divisible by 15.
Therefore,
1365 is divisible by 1, 3, 5, 7, 13, and 15.