Question

Test 85,743 for divisibility by which of the following?

a) 3, 5, 10
b) 3, 5
c) 0
d) 2, 3
e) 3, 9

Answer 1

The number 85,743 is only divisible by 3, since the sum of its digits is 27, which is divisible by 3. It is not divisible by 5 or 10 as the last digit is not 0 or 5, nor is it divisible by 9 since 27 is not divisible by 9.

Step-by-step explanation:

Divisibility Test for 85,743

To test 85,743 for divisibility by the numbers 3, 5, and 10, we apply the following divisibility rules:

• Divisibility by 3: If the sum of the digits is divisible by 3, the number is divisible by 3. In 85,743, the sum of the digits is 8+5+7+4+3 = 27, which is divisible by 3. Hence, 85,743 is divisible by 3.
• Divisibility by 5: If the last digit is 0 or 5, the number is divisible by 5. Since the last digit of 85,743 is 3, it is not divisible by 5.
• Divisibility by 9: Similar to the rule for 3, if the sum of the digits is divisible by 9, the number is divisible by 9. Since 27 is not divisible by 9, 85,743 is not divisible by 9.
• Divisibility by 10: If the last digit is 0, the number is divisible by 10. As the last digit of 85,743 is 3, it is not divisible by 10.

Therefore, 85,743 is only divisible by 3.