Prime Factorization Worksheets - Page 15

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

Solution:

From the factor tree, 216 = 8 × 27.

The quotient obtained when 216 divided by 27 is 8.

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

Solution:

From the factor tree, a = 3 × 18 = 54
[Multiply 3 and 18.]

From the factor tree, 18 = b × c

18 = 2 × 9 = 3 × 6
[Express 18 as the product of two numbers.]

The values of a, b and c are 54, 2 and 9.

143.
Which factor tree has the largest factor string?

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 4

Solution:

24 = 2 x 2 x 2 x 3
[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.

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

Solution:

In Figure - 1, the number in the box at the second level from the top of the tree = 2 × 2 = 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.

145.
Is 15 a prime or a composite number?
 a. composite b. prime c. even prime d. neither prime nor composite

Solution:

To find whether 15 is a prime or composite, draw the rectangles from exactly 15 squares.

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.