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Take the prime factorization math test! In the study of mathematics, the prime factorization of a number is achieved when we figure out what prime numbers multiply for us to find it. That can be as many as two numbers in an equation or as many as it possibly takes to reach it. See how well you understand this notion by taking the quiz below!
Questions and Answers
1.
Is 16 prime number or composite number?
Explanation A composite number is a positive integer greater than 1 that has more than two factors. In the case of 16, it can be divided evenly by numbers other than 1 and itself, such as 2, 4, and 8. Since 16 has factors other than 1 and itself, it is considered a composite number.
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2.
2^{3} x 3 =
Explanation In the expression 2^3 *3 means 2 raised to the power of 3, which is 8. Multiplying 8 by 3 gives the result 24. Therefore, the expression simplifies to 24, indicating that 2 cubed, multiplied by 3, equals 24.
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3.
Determine the prime factorization of 150.
A.
2^1 × 3^1 × 5^2
B.
2^2 × 3^2 × 5^2
C.
2 × 3 × 5^2
D.
2^3 × 3^1 × 5^2
Correct Answer
C. 2 × 3 × 5^2
4.
What is the prime factorization of 93?
A.
3 x 30
B.
3 x 31
C.
3 x 3 x 3 x 3
Correct Answer
B. 3 x 31
Explanation The prime factorization of a number involves breaking down the number into its prime factors. In this case, the prime factorization of 93 is 3 x 31. This means that 93 can be expressed as the product of the prime numbers 3 and 31.
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5.
What is the prime factorization of 56?
A.
7 x 8
B.
2 x 4 x 7
C.
2 x 2 x 2 x 7
Correct Answer
C. 2 x 2 x 2 x 7
Explanation The prime factorization of 56 is 2 x 2 x 2 x 7. This is because 56 can be divided by 2 three times, resulting in 8, and then by 7, resulting in a final quotient of 1. Therefore, the prime factors of 56 are 2 and 7, each occurring multiple times.
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6.
What is the prime factorization of 45?
A.
3 x 3 x 5
B.
5 x 9
C.
2 x 3 x 5
Correct Answer
A. 3 x 3 x 5
Explanation The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 45 can be broken down into the prime factors 3, 3, and 5. This means that when you multiply these prime factors together (3 x 3 x 5), you get the original number 45.
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7.
What is the prime factorization of 120?
A.
20 x 5
B.
2 x 2 x 3 x 5
C.
2 x 2 x 2 x 3 x 5
Correct Answer
C. 2 x 2 x 2 x 3 x 5
Explanation The prime factorization of 120 is 2 x 2 x 2 x 3 x 5. This means that 120 can be expressed as the product of these prime numbers: 2, 2, 2, 3, and 5.
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8.
Making a factor tree is a way to demonstrate the prime factorization of a number.
A.
True
B.
False
Correct Answer
A. True
Explanation Making a factor tree is indeed a way to demonstrate the prime factorization of a number. In a factor tree, the given number is broken down into its prime factors by repeatedly dividing it by prime numbers until only prime factors remain. This method helps in understanding the prime factors of a number and can be used to find the greatest common divisor or least common multiple of multiple numbers. Therefore, the statement "Making a factor tree is a way to demonstrate the prime factorization of a number" is true.
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9.
7^{5} = 7 x 5
A.
True
B.
False
Correct Answer
B. False
Explanation The given statement "75 = 7 x 5" is false. In reality, 75 is not equal to the product of 7 and 5. The correct multiplication of 7 and 5 is 35, not 75. Therefore, the answer is false.
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10.
9^{ 4} = 9 x 9 x 9 x 9
A.
True
B.
False
Correct Answer
A. True
Explanation The given equation states that 9 raised to the power of 4 is equal to multiplying 9 by itself four times. This is true because when we raise a number to a power, we are essentially multiplying that number by itself the number of times indicated by the power. In this case, 9 raised to the power of 4 means multiplying 9 by itself four times, resulting in 9 x 9 x 9 x 9, which is equal to 6561. Therefore, the statement is true.
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