If the given number is divisible by 2, 3, 4, 5, 6, 9, or 10, enter a checkmark in t...

If the given number is divisible by 2, 3, 4, 5, 6, 9, or 10, enter a checkmark in the box. See Example 6.

Reference Example 6

Is 534,840 divisible by:

a. 2 b. 3 c. 4 d. 5 e. 6 f. 9 g. 10

Strategy We will look at the last digit, the last two digits, and the sum of the digits of each number.

Why The divisibility rules call for these types of examination.

Solution

a. 534,840 is divisible by 2, because its last digit 0 is divisible by 2.

b. 534,840 is divisible by 3, because the sum of its digits is divisible by 3.

5 + 3 + 4 + 8 + 4 + 0 = 24 and 24 + 3 = 8

c. 534,840 is divisible by 4, because the number formed by its last two digits is divisible by 4.

40 ÷ 4 = 10

d. 534,840 is divisible by 5, because its last digit is 0 or 5.

e. 534,840 is divisible by 6, because it is divisible by 2 and 3. (See parts a and b.)

f. 534,840 is not divisible by 9, because the sum of its digits is not divisible by 9. There is a remainder.

24 ÷ 9 = 2 R 6

g. 534,840 is divisible by 10, because its last digit is 0.