Prime and Composite

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Prime and Composite · Grade 4 · Worksheet 2

1. Is 37 a prime number? Answer: yes Solution: A prime number has only two factors: 1 and itself. Step 2: Find the square root of 37. sqrt(37) is about 6.08.
   Full step-by-step solution

   Step 1: A prime number has only two factors: 1 and itself. Step 2: Find the square root of 37. sqrt(37) is about 6.08. So we only need to test prime numbers less than or equal to 6: 2, 3, and 5. Step 3: Test divisibility by 2. 37 is odd, so it is not divisible by 2. Step 4: Test divisibility by 3. Sum of digits: 3 + 7 = 10. 10 is not divisible by 3, so 37 is not divisible by 3. Step 5: Test divisibility by 5. The last digit of 37 is 7, not 0 or 5, so it is not divisible by 5. Step 6: Since no prime number less than or equal to sqrt(37) divides 37 evenly, 37 has no factors other than 1 and itself. Therefore, 37 is a prime number. The answer is yes.

2. Emma is organizing her sticker collection into equal groups for a school project. She has 121 stickers total. If she tries to make groups with exactly 11 stickers in each group, will she be able to use all her stickers with none left over? Explain why or why not. Answer: Yes, because 121 divided by 11 equals 11 exactly with no remainder. Solution: Understand that we need to check if 121 can be divided evenly by 11 Calculate 121 ÷ 11 11 × 11 = 121 Since 121 ÷ 11 = 11 exactly with no remainder, Emma can make 11 groups with 11 stickers each All 121 stickers will be used with none left over The answer is Yes, because 121 divided by 11 equals…
   Full step-by-step solution

   Step 1: Understand that we need to check if 121 can be divided evenly by 11 Step 2: Calculate 121 ÷ 11 Step 3: 11 × 11 = 121 Step 4: Since 121 ÷ 11 = 11 exactly with no remainder, Emma can make 11 groups with 11 stickers each Step 5: All 121 stickers will be used with none left over The answer is Yes, because 121 divided by 11 equals 11 exactly with no remainder.

3. Emma is organizing her rock collection into display cases. She has 127 rocks and wants to arrange them into equal rows. If she tries to make 7 equal rows, will she have any rocks left over? Explain how you know. Answer: Yes, she will have 1 rock left over Solution: Emma has 127 rocks and wants to make 7 equal rows To check if 127 is divisible by 7, we can divide 127 by 7 7 × 18 = 126 127 - 126 = 1 Since there is a remainder of 1, Emma will have 1 rock left over after making 7 equal rows Each row would have 18 rocks, and 1 rock would remain Therefore, Emma…
   Full step-by-step solution

   Step 1: Emma has 127 rocks and wants to make 7 equal rows Step 2: To check if 127 is divisible by 7, we can divide 127 by 7 Step 3: 7 × 18 = 126 Step 4: 127 - 126 = 1 Step 5: Since there is a remainder of 1, Emma will have 1 rock left over after making 7 equal rows Step 6: Each row would have 18 rocks, and 1 rock would remain Therefore, Emma will have 1 rock left over.

4. Is 83 a prime number or a composite number? Answer: prime Solution: A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. Find the square root of 83.
   Full step-by-step solution

   Step 1: A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. Step 2: Find the square root of 83. sqrt(83) is about 9.1, so we only need to test prime numbers less than or equal to 9: 2, 3, 5, and 7. Step 3: Test divisibility by 2. 83 is odd, so it is not divisible by 2. Step 4: Test divisibility by 3. Sum of digits: 8 + 3 = 11. 11 is not divisible by 3, so 83 is not divisible by 3. Step 5: Test divisibility by 5. The last digit of 83 is 3, not 0 or 5, so it is not divisible by 5. Step 6: Test divisibility by 7. 7 × 11 = 77 and 7 × 12 = 84. 83 is not a multiple of 7. Step 7: No prime numbers less than or equal to 9 divide 83 evenly. The only factors of 83 are 1 and 83. Step 8: Since 83 has exactly two factors, it is a prime number. The answer is prime.

5. Emma is organizing her rock collection into display cases. She has 127 rocks and wants to arrange them into equal rows. If she tries to make 3 equal rows, will she have any rocks left over? Explain how you know. Answer: Yes, she will have 1 rock left over because 127 divided by 3 has a remainder of 1. Solution: To determine if 127 can be divided into 3 equal rows with no remainder, we need to check if 127 is divisible by 3. One way to check divisibility by 3 is to add up all the digits of the number: 1 + 2 + 7 = 10.
   Full step-by-step solution

   Step 1: To determine if 127 can be divided into 3 equal rows with no remainder, we need to check if 127 is divisible by 3. Step 2: One way to check divisibility by 3 is to add up all the digits of the number: 1 + 2 + 7 = 10. Step 3: Check if this sum (10) is divisible by 3: 10 ÷ 3 = 3 with remainder 1. Step 4: Since the sum of the digits (10) is not divisible by 3, the original number (127) is also not divisible by 3. Step 5: To find how many rocks would be left over, divide 127 by 3: 127 ÷ 3 = 42 with remainder 1. Step 6: This means Emma can make 42 rocks in each of 3 rows, with 1 rock left over. The answer is: Yes, she will have 1 rock left over.

6. A rectangular garden is drawn with a length of 12 meters and a width of 8 meters. The gardener plants a square flower bed in one corner that is 3 meters on each side. What is the area of the remaining part of the garden, in square meters? Answer: 87 Solution: Find the total area of the rectangular garden. The garden length is 12 meters and width is 8 meters. Area of rectangle = length × width Area = 12 × 8 = 96 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden. The garden length is 12 meters and width is 8 meters. Area of rectangle = length × width Area = 12 × 8 = 96 square meters. Step 2: Find the area of the square flower bed. The flower bed is a square with side length 3 meters. Area of square = side × side Area = 3 × 3 = 9 square meters. Step 3: Subtract the flower bed area from the total garden area to find the remaining area. Remaining area = total garden area − flower bed area Remaining area = 96 − 9 = 87 square meters. Step 4: State the final answer. The area of the remaining part of the garden is 87 square meters.

7. Is 57 a prime number? Answer: no Solution: A prime number has only two factors: 1 and itself. We need to check if 57 has any other factors. The square root of 57 is about 7.5, so we only need to test prime numbers up to 7: 2, 3, 5, and 7.
   Full step-by-step solution

   Step 1: A prime number has only two factors: 1 and itself. We need to check if 57 has any other factors. Step 2: The square root of 57 is about 7.5, so we only need to test prime numbers up to 7: 2, 3, 5, and 7. Step 3: Check divisibility by 2: 57 is odd, so it is not divisible by 2. Step 4: Check divisibility by 3: The sum of the digits is 5 + 7 = 12. Since 12 is divisible by 3, 57 is divisible by 3. Step 5: 57 ÷ 3 = 19. So 57 = 3 × 19. It has factors other than 1 and itself. Step 6: Therefore, 57 is a composite number. The answer is no.