Magic Numbers: Factors, Primes And Composites Quiz

Prime numbers are numbers that can only be divided by 1 and themselves without leaving a remainder. This means that prime numbers do not have any other factors except for 1 and the number itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers because they cannot be divided evenly by any other numbers except for 1 and the number itself.

Prime numbers have exactly 2 factors. This is because a prime number is only divisible by 1 and itself. Therefore, there are no other numbers that can evenly divide a prime number, resulting in exactly 2 factors.

A factor is defined as one or two whole numbers that multiply together to give a product. It is not necessarily a prime number, nor is it related to addition or subtraction. Factors are used to divide a number evenly and are an important concept in mathematics.

The factors of a number are the numbers that can divide it evenly without leaving a remainder. In this case, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. These numbers can all divide 36 without leaving a remainder.

A composite number is a number that has more than two factors. This means that it can be divided evenly by at least two different numbers, in addition to one and itself. For example, the number 12 is a composite number because it can be divided evenly by 1, 2, 3, 4, 6, and 12. In contrast, a prime number only has two factors, 1 and itself. Therefore, the correct answer is "A number with 2 or more factors."

To create multiples of a number, you multiply the multiple by another factor (i.e., you perform multiplication using the original number and a different factor). For example, if you want to create multiples of 5, you can multiply 5 by 2, 3, 4, etc., to generate the multiples 10, 15, 20, and so on.

The number 72 has 12 factors because it can be divided evenly by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. It also has 11 proper factors because it excludes the number itself, so the proper factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36. Therefore, the statement is true.

The correct answer is "a number that can be divided by another number without a remainder." This is because when we say a number is "multiple" of another number, it means that the first number is divisible by the second number without leaving any remainder. In other words, the first number can be expressed as the product of the second number and some integer.

The correct answer is 1, 2, 4, 8, 16, and 32. The factors of a number are the numbers that can divide evenly into that number without leaving a remainder. In this case, the factors of 32 are 1, 2, 4, 8, 16, and 32 because these numbers can all divide evenly into 32.

In Method 2 for creating multiples, the correct approach is to add the multiple to the previous answer or product. This means that each time a multiple is generated, it should be added to the previous answer or product to obtain the next multiple. This method ensures that the multiples are incrementally generated by continuously adding the same value to the previous result.

When writing the proper factor or a number, you do not include the number itself because a proper factor is a factor of a number that is less than the number itself. For example, the proper factors of 6 are 1, 2, and 3, but 6 is not considered a proper factor because it is the number itself.

The correct answer is 72, 216. The question asks for a list of multiples, and the given answer provides two numbers that are multiples of the missing numbers in the list. The numbers 72 and 216 are both multiples of 72, and 216 is also a multiple of 144. Therefore, the answer correctly completes the multiples list.

The proper factors of a number are all the factors of that number except for the number itself. In this case, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. However, since we are looking for proper factors, we exclude 24 from the list. Therefore, the proper factors of 24 are 1, 2, 3, 4, 6, 8, and 12.

The given answer lists the proper factors of 72 in ascending order from least to greatest, separated by commas. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

A prime number is a whole number greater than 1 that has only two factors (divisors): 1 and itself. The numbers 2, 3, 5, 7, 11, 13, 17, and 19 all fit this definition as they cannot be divided evenly by any other whole number.

The factors of 120 are all the numbers that can divide evenly into 120 without leaving a remainder. In this case, the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The factors are listed in numerical order, separated by commas.

Multiples of a number are found by multiplying the number by integers (1, 2, 3, 4, and so on). The first five multiples of 64 are:

64 × 1 = 64,

64 × 2 = 128,

64 × 3 = 192,

64 × 4 = 256,

64 × 5 = 320.

Hence, the correct answer is 64, 128, 192, 256, and 320.