Fundamentals of Mathematics, 2008a

177
31 is not divisible by 2 Its last digit is not even
31 ÷ 2 = 15R1
The quotient, 15, is larger than the divisor, 3. Continue.
31 is not divisible by 3 The digits 3 + 1 = 4, and 4 is not divisible by 3.
31 ÷ 3 = 10R1
The quotient, 10, is larger than the divisor, 3. Continue.
31 is not divisible by 5 The last digit of 31 is not 0 or 5.
31 ÷ 5 = 6R1
The quotient, 6, is larger than the divisor, 5. Continue.
31 is not divisible by 7. Divide by 7.
31 ÷ 7 = 4R1
The quotient, 4, is smaller than the divisor, 7.
We can stop the process and conclude that 31 is a prime number.
The number 31 is a prime number
3.4.6.2 Practice Set C
Find the prime factorization of each whole number.
Exercise 3.4.16 (Solution on p. 204.)
22
Exercise 3.4.17 (Solution on p. 204.)
40
Exercise 3.4.18 (Solution on p. 204.)
48
Exercise 3.4.19 (Solution on p. 204.)
63
Exercise 3.4.20 (Solution on p. 204.)
945
Exercise 3.4.21 (Solution on p. 204.)
1,617
Exercise 3.4.22 (Solution on p. 204.)
17
Exercise 3.4.23 (Solution on p. 204.)
61
3.4.7 Exercises
For the following problems, determine the missing factor(s).
Exercise 3.4.24 (Solution on p. 204.)
14=7·
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