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Problem 1: The area the a rectangle-shaped garden is 7 square yards. List all possible whole-number size the garden have the right to 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, space the factors of the number 7.

Problem 2: The area of a rectangular garden is 8 square yards. Perform all feasible whole-number size 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 also 8, of the rectangular gardens in difficulty 2, room the factors of the number 8. In trouble 1, the number 7 has actually only two factors. The number 7 is prime. In trouble 2 above, the number 8 has four factors. The number 8 is composite.

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

When the area of a rectangle is a element number, over there is only one set of possible dimensions for that rectangle. When the area the a rectangle is a composite number, there are two or an ext sets of feasible dimensions for that rectangle. Each set of dimensions is a pair the factors.

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

Find all determinants of the number.If the number has only 2 factors, 1 and itself, then it is prime.If the number has more than 2 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 are 1 x 9, 3 x 3. 9 is composite.

We have identified if a single number is element or composite. Let"s look in ~ a variety of number to see if they space prime or composite. Please keep in mind that each variety of numbers offered in examples 3, 4 and 5 listed below are inclusive.

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

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

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

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

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

Solution: The prime numbers between 10 and also 19 room 11, 13, 17 and also 19. 

Example 5: Find all prime numbers in between 20 and 29.

factors of 20:1 x 20, 2 x 10, 4 x 520 is composite
factors of 21:1 x 21, 3 x 721 is composite
factors that 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 that 25:1 x 25, 5 x 525 is composite
factors that 26:1 x 26, 2 x 1326 is composite
factors the 27:1 x 27, 3 x 927 is composite
factors the 28:1 x 28, 2 x 14, 4 x 728 is composite
factors that 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 prize using complete sentences.

Solution 1: The number 31 is prime because its only factors are one and also 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 also 31 and also found no factors other than one and thirty-one. Therefore, 31 is prime.

There room many feasible ways to describe the equipment to this problem. This are just three feasible explanations.

Summary: A element number has only 2 factors: 1 and also itself. A composite number has more than two factors. The number 1 is neither prime no one composite. 

The element numbers 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 actually only two factors, itself and 1.

Exercises

Directions: check out each inquiry below. Pick your answer by clicking on its button. Feedback to her answer is noted in the outcomes BOX. If you make a mistake, pick a different button.

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

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

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

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

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5.

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

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