Hayley has 16 square boxes to make an array of rectangular shapes on a grid. Harry says if she uses 19 square boxes she will get more arrays. Do you aree or disagree with Harrys' claim? Explain your answer using prime and composite numbers. Use the drawings of the rectangles in your answer.

Question

Hayley has 16 square boxes to make an array of rectangular shapes on a grid. Harry says if she uses 19 square boxes she will get more arrays. Do you aree or disagree with Harrys' claim? Explain your answer using prime and composite numbers. Use the drawings of the rectangles in your answer.

Answer 1

We cannot draw figures for you, and it It is not clear what you mean by an "array". Does it have to be rectangular N x M array with all elements filled by a box? If so, you can make more arrays with 16 because it is not a prime number.

19 -> 1 x 19 or 19 x 1
16 -> 1 x 16, 16 x 1, 2 x 8, 8 x 2, and 4 x 4

Answer 2

19->1]^.>~>|\352564

Answer 3

To determine whether Harry's claim is true or false, we need to understand the relationship between the number of square boxes and the arrays of rectangular shapes Hayley can make.

First, let's consider a simple scenario using prime and composite numbers. Prime numbers are numbers that have only two factors, 1 and the number itself. For example, 2, 3, 5, and 7 are prime numbers. Composite numbers, on the other hand, have more than two factors. For example, 4, 6, 8, and 9 are composite numbers.

Now, let's break down the problem using these concepts.

1) Hayley has 16 square boxes to make an array of rectangular shapes on a grid. To determine the possibilities, we need to find all the factor pairs of 16.

The factor pairs of 16 are:
1 x 16 = 16
2 x 8 = 16
4 x 4 = 16

We can create three different arrays with 16 square boxes. Let's represent them with rectangles:

Array 1:
XXXX
XXXX

Array 2:
XXXXXXXX

Array 3:
XXXX
XXXX

2) Next, Harry claims that if Hayley uses 19 square boxes, she will get more arrays. To verify this claim, we need to find all the factor pairs of 19.

The factor pairs of 19 are:
1 x 19 = 19

Since 19 is a prime number, it only has one factor pair. Therefore, there is only one possible array with 19 square boxes. Let's represent it with a rectangle:

Array 4:
XXXXXXXXX

From this analysis, it is clear that Hayley can create more arrays using 16 square boxes than using 19 square boxes. The use of prime numbers in this scenario helps us understand that having more factors (such as in the case of 16) grants more possibilities for forming arrays of rectangular shapes.