Prime Factorization Worksheets

**Page 15**

141.

Using the factor tree, find the quotient obtained when 216 is divided by 27.

a. | 9 | ||

b. | 4 | ||

c. | 3 | ||

d. | 8 |

The quotient obtained when 216 divided by 27 is 8.

Correct answer : (4)

142.

Find the values of $a$, $b$ and $c$ in the factor tree.

a. | 21, 2, 9 | ||

b. | 54, 2, 9 | ||

c. | 15, 2, 9 | ||

d. | 318, 1, 8 |

[Multiply 3 and 18.]

From the factor tree, 18 =

18 = 2 × 9 = 3 × 6

[Express 18 as the product of two numbers.]

The values of

Correct answer : (2)

143.

Which factor tree has the largest factor string?

a. | Figure 1 | ||

b. | Figure 2 | ||

c. | Figure 3 | ||

d. | Figure 4 |

[Write the prime factorization of 24 from figure 1.]

72 = 2 x 2 x 2 x 3 x 3

[Write the prime factorization of 72 from figure 2.]

125 = 5 x 5 x 5

[Write the prime factorization of 125 from figure 3.]

81 = 3 x 3 x 3 x 3

[Write the prime factorization of 81 from figure 4.]

72 has more factors than any other number.

The factor tree for 72 represented by the figure in the choice B has the largest factor string.

Correct answer : (2)

144.

Which of the factor trees model(s) an even number?

a. | Figure - 1 | ||

b. | Figure - 2 | ||

c. | Figure - 1 & Figure - 3 | ||

d. | Figure - 1, Figure - 3 & Figure - 4 |

The number at the top of the tree = 16 × 4 = 64.

In Figure - 2, the number in the box at the second level of the tree from top = 5 × 3 = 15.

The number at the top of the tree = 5 × 15 = 75.

In Figure - 3, the number in the box at the second level from the top of the tree = 2 × 4 = 8.

The number at the top of the tree = 8 × 8 = 64.

In Figure - 4, the number at the top of the tree = 13 × 4 = 52.

The factor trees in Figure 1, 3 & 4 model an even number.

Correct answer : (4)

145.

Is 15 a prime or a composite number?

a. | composite | ||

b. | prime | ||

c. | even prime | ||

d. | neither prime nor composite |

The following graph shows that two rectangles of dimensions 3 x 5 and 15 x 1 can be drawn from 15 squares.

The dimensions of the rectangle show that the factors of 15 are 1, 3, 5 and 15.

A number that has more than two factors is called a composite number.

So, 15 is a composite number.

Correct answer : (1)