Chapter 4: Section 1:Divisibility and Factors

By Ms. Dewey-HoffmanDecember 1st, 2009

Warm Ups for Chapter 4

• Find the Quotient: 147 3 =

• Find the Quotient: 273/3 =

• Find the Quotient: 450/10 =

• Find the Product: 4 • 4 • 4 =

• Find the Product: (-2)(-2)(-2) =

• Find the Product: (10)(10)(10)(10) =

Warm Ups for Chapter 4

• Write TWO numbers, that when multiplied together, give this product:

• 12

• 50

• 36

• 24

Section 4.1: Divisibility and Factors

• One integer is DIVISIBLE by another if the remainder is 0 when you divide.

• Divisibility Rules for 2, 5, and 10.

An integer is divisible by…

• 2, if it ends in 0, 2, 4, 6, and 8.

• 5, if it ends in 0 or 5.

• 10, if it ends in 0.

Examples: Divisibility Rules

• Is the first number divisible by the second?

• 567 and 2?

• 1,015 and 5?

• 111,120 and 10?

• 53 and 2?

• 1,118 and 2?

Divisibility Rule for 3 and 9.

• See if you can pick out the pattern…

Number

Sum of Digits

Is the Sum Divisible by:

3? 9?

Is the Number

Divisible by:

3? 9?

282 2 + 8 + 2 = 12 Yes No Yes No

468 4 + 6 + 8 = 18 Yes Yes Yes Yes

215 2 + 1 + 5 = 8 No No No No

1,017 1 + 0 + 1 + 7 = 9

Yes Yes Yes Yes

Divisibility Rule for 3 and 9.

• From the pattern we saw before…

• An integer is divisible by…

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

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

Example Problems:

• Is the first number divisible by the second? Explain.

• 64 by 9?

• 472 by 3?

• 174 by 3?

• 43,542 by 9?

Finding Factors

•One integer is a FACTOR of another integer if it divides that integer with remainder zero.

number

numbernumber

Finding Factors

• So find all the different combinations of factors

• 12?

• 16?

• 18?

• 24?

1(12), 2(6), 3(4): so, 1, 2, 3, 4, 6, and 12

1(16), 2(8), 4(4): so, 1, 2, 4, 8, and 16

1(18), 2(9), 3(6): so, 1, 2, 3, 6, 9, and 18

1(24), 2(12), 3(8), 4(6): so, 1, 2, 3, 4, 6, 8, 12, and 24

Word Problem:

• There are 20 choral students singing at a school concert. Each row of singers much have the same number of students. If there are at least 5 students in each row, what are all the possible arrangements?

List the positive factors of each number.

• 10

• 21

• 31

1, 2, 5, 10

1, 3, 7, 21

1, 31

Homework #40

• USE YOUR NOTES TO REMIND YOU OF THE DIVISIBILITY RULES!!!

• Page 174: 6-35 all.