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Problem 1: The area the a rectangle-shaped garden is 7 square yards. Perform all feasible whole-number size the garden can have.

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Solution: 1 yd x 7 yd

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

Problem 2: The area of a rectangular garden is 8 square yards. Perform all possible whole-number size the garden can 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, of the rectangle-shaped gardens in trouble 2, are the factors of the number 8. In trouble 1, the number 7 has only 2 factors. The number 7 is prime. In problem 2 above, the number 8 has 4 factors. The number 8 is composite.

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

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

To recognize if a number is element or composite, follow this steps:

Find all components 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, climate it is composite.

Example 1: Is the number 2 prime or composite?

Solution: The components 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 solitary number is element or composite. Let"s look at a range of number to check out if they room prime or composite. Please keep in mind that each range of numbers offered in instances 3, 4 and 5 listed below are inclusive.

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

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

Solution: The prime numbers between 2 and also 9 are 2, 3, 5 and also 7. 

Example 4: Find every prime numbers in between 10 and also 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 of 13:1 x 1313 is prime
factors that 14:1 x 14, 2 x 714 is composite
factors that 15:1 x 15, 3 x 515 is composite
factors the 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 the 19:1 x 1919 is prime

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

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

factors of 20:1 x 20, 2 x 10, 4 x 520 is composite
factors that 21:1 x 21, 3 x 721 is composite
factors the 22:1 x 22, 2 x 1122 is composite
factors the 23:1 x 2323 is prime
factors the 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 of 26:1 x 26, 2 x 1326 is composite
factors of 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 29 space 23 and 29. 

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Example 6: Is the number 31 prime or composite? explain your answer using complete sentences.

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

Solution 2: Thirty-one is a element number. This is since the number 31 has only 2 factors: 1 and also 31.

Solution 3: I separated the number 31 by all numbers in between 1 and 31 and found no factors other 보다 one and also thirty-one. Therefore, 31 is prime.

There are many feasible ways to explain the systems to this problem. These are simply three feasible explanations.

Summary: A prime number has only two factors: 1 and also itself. A composite number has an ext than 2 factors. The number 1 is no prime no one composite. 

The element numbers in between 2 and also 31 space 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 because each of this numbers has actually only two factors, itself and also 1.

Exercises

Directions: read each question below. Pick your answer by clicking its button. Feedback to her answer is noted in the results BOX. If you make a mistake, pick a different button.

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

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2.The element numbers between 40 and also 49 are:42, 43 and also 4741, 43 and 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 5951 and 59 53 and also 57None of 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 of the above.

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5.

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

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