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Problem 1: The area of a rectangular garden is 7 square yards. List all possible whole-number size the garden can have.

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Solution: 1 yd x 7 yd

The whole-number dimensions, 1 and also 7, of the rectangle-shaped garden above, room the factors of the number 7.

Problem 2: The area that a rectangular garden is 8 square yards. Perform all feasible whole-number dimensions the garden deserve to have.

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Solution: 1 yd x 8 yd, 2 yd x 4 yd

The whole-number dimensions, 1, 2, 4 and 8, the the rectangular gardens in difficulty 2, room the factors of the number 8. In problem 1, the number 7 has only 2 factors. The number 7 is prime. In trouble 2 above, the number 8 has 4 factors. The number 8 is composite.

Definitionsprime number has only two factors: 1 and itself.A composite number has more than 2 factors.The number 1 is neither prime nor composite.

When the area that a rectangle is a element number, there is just one collection of possible dimensions for that rectangle. As soon as the area of a rectangle is a composite number, there room two or more sets of possible dimensions for the rectangle. Each set of dimensions is a pair that factors.

To identify if a number is prime or composite, follow this steps:

Find all components of the number.If the number has actually only two factors, 1 and also itself, then it is prime.If the number has more than two factors, then it is composite.

Example 1: Is the number 2 element or composite?

Solution: The determinants of 2 are 1 x 2. 2 is prime.

Example 2: Is the number 9 element or composite?

Solution: The determinants of 9 space 1 x 9, 3 x 3. 9 is composite.

We have established if a solitary number is prime or composite. Let"s look at a range of numbers to check out if they space prime or composite. Please note that each variety of numbers given in instances 3, 4 and 5 below are inclusive.

Example 3: Find all prime numbers between 2 and also 9.

factors the 2:1 x 22 is prime
factors that 3:1 x 33 is prime
factors of 4:1 x 4, 2 x 24 is composite
factors of 5:1 x 55 is prime
factors of 6:1 x 6, 2 x 36 is composite
factors of 7:1 x 77 is prime
factors the 8:1 x 8, 2 x 48 is composite
factors that 9:1 x 9, 3 x 39 is composite

Solution: The element numbers in between 2 and 9 room 2, 3, 5 and also 7. 

Example 4: Find all prime numbers in between 10 and 19.

factors the 10:1 x 10, 2 x 510 is composite
factors of 11:1 x 1111 is prime
factors that 12:1 x 12, 2 x 6, 3 x 412 is composite
factors the 13:1 x 1313 is prime
factors the 14:1 x 14, 2 x 714 is composite
factors that 15:1 x 15, 3 x 515 is composite
factors of 161 x 16, 4 x 416 is composite
factors that 17:1 x 1717 is prime
factors that 18:1 x 18, 3 x 618 is composite
factors of 19:1 x 1919 is prime

Solution: The element numbers in between 10 and also 19 are 11, 13, 17 and 19. 

Example 5: Find every prime numbers between 20 and also 29.

factors the 20:1 x 20, 2 x 10, 4 x 520 is composite
factors the 21:1 x 21, 3 x 721 is composite
factors the 22:1 x 22, 2 x 1122 is composite
factors of 23:1 x 2323 is prime
factors that 24:1 x 24, 2 x 12, 3 x 8, 4 x 624 is composite
factors the 25:1 x 25, 5 x 525 is composite
factors that 26:1 x 26, 2 x 1326 is composite
factors of 27:1 x 27, 3 x 927 is composite
factors that 28:1 x 28, 2 x 14, 4 x 728 is composite
factors the 29:1 x 2929 is prime

Solution: The prime numbers in between 20 and also 29 space 23 and 29. 

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Example 6: Is the number 31 element or composite? describe your price using full sentences.

Solution 1: The number 31 is prime due to the fact that its only determinants are one and itself.

Solution 2: Thirty-one is a element number. This is due to the fact that the number 31 has only 2 factors: 1 and 31.

Solution 3: I divided the number 31 by all numbers in between 1 and 31 and found no components other than one and thirty-one. Therefore, 31 is prime.

There space many feasible ways to define the solution to this problem. These are just three feasible explanations.

Summary: A prime number has only 2 factors: 1 and also itself. A composite number has more than 2 factors. The number 1 is no prime nor composite. 

The element numbers in between 2 and 31 space 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and also 31 due to the fact that each of these numbers has only 2 factors, itself and 1.

Exercises

Directions: review each question below. Pick your prize by clicking on its button. Feedback to your answer is detailed in the results BOX. If you make a mistake, choose a different button.

1.Each of the adhering to numbers is composite EXCEPT:30, 31, 32, 33, 34, 35, 36, 37, 38, 3932 and 3930 and also 3431 and also 37All composite

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2.The prime numbers in between 40 and 49 are:42, 43 and also 4741, 43 and also 47 43, 45 and also 47None the the above.

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3.The element numbers between 50 and also 59 are:53 and also 5951 and also 59 53 and also 57None the the above.

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4.The prime numbers in between 60 and 69 are:63 and 6961 and also 67 60 and also 65None of the above.

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5.

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The element numbers between 20 and 69 are:21, 23, 29, 31, 37, 41, 43, 47, 53, 63 and also 6923, 29, 31, 33, 37, 41, 43, 47, 59, 61 and 6723, 29, 31, 37, 41, 43, 47, 53, 59, 61 and also 67None the the above.

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