Factors and Multiples 6.7A and 6.7D

Find a common factor based on the map's instructions.

• The map suggests that a common factor is a number that can be subtracted from their numbers without leaving a remainder.

• The map suggests that a common factor is a number that can be added to their numbers without leaving a remainder.

• The map suggests that a common factor is a number that can be multiplied with their numbers without leaving a remainder.

• The map suggests that a common factor is a number that can be divided by their numbers without leaving a remainder.

Answer explanation

The map suggests that a common factor is a number that allows Bryant, Kaylee, and Nathaniel to divide their numbers without leaving a remainder.

Nathaniel, Miguel, and Kaylee want to distribute their chocolates equally. They need to find the greatest common factor (GCF) of the number of chocolates they each have. What does this mean?

• The GCF is the smallest number of chocolates that can be evenly divided among them.

• The GCF is the total number of chocolates they have together.

• The GCF is the average number of chocolates they each have.

• The GCF is the largest number of chocolates that can be evenly divided among them.

Answer explanation

The greatest common factor (GCF) is the largest number of chocolates that can be evenly divided among Nathaniel, Miguel, and Kaylee.

Which of the following statements correctly defines a prime number?

• A prime number is a number that is divisible by 1 and all other numbers except itself.

• A prime number is a number greater than 1 that is divisible only by 1 and itself.

• A prime number is a number that is divisible by 2 and itself.

• A prime number is a number that is divisible by all other numbers except 1 and itself.

Answer explanation

A prime number is a number greater than 1 that is divisible only by 1 and itself.

Which statement correctly defines composite numbers?

• Composite numbers are fractions that have at least one divisor other than 1 and itself.

• Composite numbers are prime numbers that have at least one divisor other than 1 and itself.

• Composite numbers are positive integers that have at least one divisor other than 1 and itself.

• Composite numbers are negative integers that have at least one divisor other than 1 and itself.

Answer explanation

Composite numbers are positive integers with at least one divisor other than 1 and itself.

Which statement best describes the concept of a multiple in the context of buying apples in a sale?

• A multiple is a number that is always greater than the number it is being divided by.

• A multiple is a number that can be divided by another number without leaving a remainder.

• A multiple is a number that can only be divided by itself.

• A multiple is a number that cannot be divided by another number without leaving a remainder.

Answer explanation

A multiple is a number of apples that can be divided without remainder.

Kaylee, Bryant, and Miguel need to find a common time interval for a meeting. What is the least common multiple (LCM) of their time intervals?

• The LCM is the average of their time intervals.

• The LCM is the smallest positive integer divisible by their time intervals without a remainder.

• The LCM is the sum of their time intervals.

• The LCM is the largest positive integer divisible by their time intervals without a remainder.

Answer explanation

The LCM is the smallest integer divisible by their time intervals without remainder.

Commutative Property

Nathaniel says that they can add the cost of apples and oranges in any order, and the total cost will be the same. What is Nathaniel explaining?

• The commutative property states that the order of the numbers does not affect the result of addition or multiplication.

• The commutative property only applies to addition.

• The commutative property only applies to multiplication.

• The commutative property states that the order of the numbers affects the result of addition or multiplication.

Answer explanation

The commutative property states that the order of the numbers does not affect the result of addition or multiplication.

What are relatively prime numbers?

• Numbers that have common factors other than 1

• Numbers that are divisible by each other

• Numbers that have no common factors other than 1

• Numbers that are not prime

Answer explanation

Relatively prime numbers are numbers that have no common factors other than 1. They are not divisible by each other and are not prime.

What does the exponent represent in the context of calculating the area of a square?

• A notation indicating the number of times a number is multiplied by itself.

• A notation indicating the number of times a number is subtracted from itself.

• A notation indicating the number of times a number is added to itself.

• A notation indicating the number of times a number is divided by itself.

Answer explanation

The exponent represents the number of times a number is multiplied by itself, which is the correct choice for calculating the area of a square.

Is the labeling of 'exponent', 'base', and 'power' correct in the equation for calculating the area of a square with side length 2 raised to the power of 3?

• yes

• no

Answer explanation

Yes, Priya's labeling is correct. The exponent refers to the power to which the base is raised, and in this case, the base is 2 and the power is 3.