Page 207 - Basic College Mathematics with Early Integers

184 C HAPTE R 3 I FRACTIONS

Divisibility Tests

A whole number is divisible by:
• 2 if the last digit is 0, 2, 4, 6, or 8.
T
132 is divisible by 2 since the last digit is a 2.
• 3 if the sum of the digits is divisible by 3.
144 is divisible by 3 since 1 + 4 + 4 = 9 is divisible by 3.

• 5 if the last digit is 0 or 5.
T
1115 is divisible by 5 since the last digit is a 5.

Here are a few other divisibility tests you may want to use. A whole number is
divisible by:
• 4 if its last two digits are divisible by 4.
1712 is divisible by 4.

• 6 if it’s divisible by 2 and 3.
9858 is divisible by 6.
• 9 if the sum of its digits is divisible by 9.
5238 is divisible by 9 since 5 + 2 + 3 + 8 = 18 is divisible by 9.

When finding the prime factorization of larger numbers, you may want to use
the procedure shown in Example 3.

PRACTICE 3 Example 3 Write the prime factorization of 252.
Write the prime factorization
of 297. Solution: For this method, we divide prime numbers into the given number.
Since the ones digit of 252 is 2, we know that 252 is divisible by 2.
126
2252
126 is divisible by 2 also.
63
2126
2252
63 is not divisible by 2 but is divisible by 3. Divide 63 by 3 and continue in this
same manner until the quotient is a prime number.

7
3 21
3 63 The order of choosing prime numbers does not
2126 matter. For consistency, we use the order 2, 3, 5, 7, Á .
2252
# # # #
2
The prime factorization of 252 is 2 2 3 3 7 or 2 2 # # 7. Copyright 2012 Pearson Education, Inc.
3
Work Practice 3
Answer
3
3. 3 # 11