Check whether the following numbers are divisible by 6.

a) 59730

b) 18620

c) 83652

d) 675083

From the checks, 59730 and 83652 are divisible by 6, while 18620 and 675083 are not. This shows the importance of checking both conditions for divisibility by 6. Thus, we can summarize that only the numbers 59730 and 83652 meet the criteria.
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Answered by Anonymous | 2025-07-04

To determine if a number is divisible by 6, it needs to satisfy two conditions: it must be divisible by 2 and by 3.

Divisibility by 2 : A number is divisible by 2 if its last digit is even (i.e., 0, 2, 4, 6, or 8).

Divisibility by 3 : A number is divisible by 3 if the sum of its digits is divisible by 3.


Now, let's check each number:
a) 59730

Divisibility by 2 : The last digit is 0, which is even.
Divisibility by 3 : The sum of the digits is 5 + 9 + 7 + 3 + 0 = 24, and 24 is divisible by 3.
Conclusion : 59730 is divisible by 6.

b) 18620

Divisibility by 2 : The last digit is 0, which is even.
Divisibility by 3 : The sum of the digits is 1 + 8 + 6 + 2 + 0 = 17, and 17 is not divisible by 3.
Conclusion : 18620 is not divisible by 6.

c) 83652

Divisibility by 2 : The last digit is 2, which is even.
Divisibility by 3 : The sum of the digits is 8 + 3 + 6 + 5 + 2 = 24, and 24 is divisible by 3.
Conclusion : 83652 is divisible by 6.

d) 675083

Divisibility by 2 : The last digit is 3, which is not even.
Conclusion : Since the number is not divisible by 2, it is not divisible by 6, regardless of its divisibility by 3.

To summarize, numbers 59730 and 83652 are divisible by 6, while 18620 and 675083 are not.

Answered by RyanHarmon181 | 2025-07-06