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Problem 1: The area the a rectangular garden is 7 square yards. List all feasible whole-number dimensions the garden deserve to have.

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Solution: 1 yd x 7 yd

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

Problem 2: The area the a rectangle-shaped garden is 8 square yards. Perform all feasible whole-number dimensions the garden have the right 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, that the rectangle-shaped gardens in problem 2, space the determinants of the number 8. In trouble 1, the number 7 has actually only two factors. The number 7 is prime. In difficulty 2 above, the number 8 has four factors. The number 8 is composite.

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

When the area of a rectangle is a element number, over there is just one collection of possible dimensions for that rectangle. As soon as the area that a rectangle is a composite number, there room two or more sets of possible dimensions for that rectangle. Each set of size 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 actually only two factors, 1 and also itself, climate it is prime.If the number has much more than two factors, climate it is composite.

Example 1: Is the number 2 element or composite?

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

Example 2: Is the number 9 prime or composite?

Solution: The factors of 9 room 1 x 9, 3 x 3. 9 is composite.

We have identified if a solitary number is prime or composite. Let"s look in ~ a selection of number to view if they room prime or composite. Please keep in mind that each range of numbers provided in instances 3, 4 and also 5 listed below are inclusive.

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

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

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

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

factors the 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 the 14:1 x 14, 2 x 714 is composite
factors the 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 the 18:1 x 18, 3 x 618 is composite
factors the 19:1 x 1919 is prime

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

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

factors that 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 that 23:1 x 2323 is prime
factors the 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 that 29:1 x 2929 is prime

Solution: The element numbers in between 20 and 29 room 23 and also 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 since its only determinants are one and itself.

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

Solution 3: I separated the number 31 by every numbers between 1 and also 31 and 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. These are simply three feasible explanations.

Summary: A element 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 between 2 and also 31 space 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 since each of these numbers has only 2 factors, itself and also 1.

Exercises

Directions: check out each inquiry below. Pick your answer by clicking on its button. Feedback to your answer is provided in the results BOX. If you do a mistake, select a various button.

1.Each the the complying with 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 in between 40 and 49 are:42, 43 and 4741, 43 and also 47 43, 45 and also 47None the the above.

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3.The prime numbers in between 50 and 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 67 60 and 65None that 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 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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