Basic Mathematics for College Students

1.5 Dividing Whole Numbers 61

the 1 from the ones column of the dividend. Ask: “How

many times will 518 divide 2,651?” We can the answer to

that question by thinking is about 5, and we write the 5 in the

ones column of the quotient. 5 and 518, and their

product, 2,590, from 2,651, to get a remainder of 61.

The result is 25 R 61. To check, verify that (25518) 61 is 13,011.

Multiply subtract

26  5

estimate

Bring down

25

(^518)  13011
 1036
2651
 2590
61
5 Use tests for divisibility.
We have seen that some divisions end with a 0 remainder and others do not. The
word divisibleis used to describe such situations.
Divisibility
One number is divisibleby another if, when dividing them, we get a remainder
of 0.
Since with a 0 remainder, we say that 27 is divisible by 3.Since
R 2, we say that 27 is not divisible by 5.
There are tests to help us decide whether one number is divisible by another.

27  5  5

27  3 9,

Tests for Divisibility

A number is divisible by

• 2 if its last digit is divisible by 2.


• 3 if the sum of its digits is divisible by 3.


• 4 if the number formed by its last two digits is divisible by 4.


• 5 if its last digit is 0 or 5.


• 6 if it is divisible by 2 and 3.


• 9 if the sum of its digits is divisible by 9.


• 10 if its last digit is 0.

There are tests for divisibility by a number other than 2, 3, 4, 5, 6, 9, or 10, but they
are more complicated. See problems 109 and 110 of Study Set 1.5 for some examples.

EXAMPLE (^6) Is 534,840 divisible by:
a. 2 b. 3 c. 4 d. 5 e. 6 f. 9 g. 10
StrategyWe will look at the last digit, the last two digits, and the sum of the
digits of each number.
WHYThe divisibility rules call for these types of examination.
Solution
a. is divisible by 2, because its last digit 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

534,84 0 0

Self Check 6

Is 73,311,435 divisible by:

a. 2 b. 3 c. 5

d. 6 e. 9 f. 10

Now TryProblems 49 and 53