097r. Factors, Multiples and Powers
Learning Intentions
- To understand that a prime number has exactly two factors and a composite number has more than two factors
- To know the meaning of the terms square, square root, cube and cube root
- Solve the lowest common multiple and highest common factor of two numbers
- find the square, square root, cube and cube root of certain small whole numbers
Pre-requisite Summary
- Know that a factor divides a number exactly with no remainder. See 010r. Factors and Multiples
- Know that a multiple is found by multiplying a number by whole numbers
- Be able to list the factors of small whole numbers
- Be able to list the multiples of small whole numbers
- Understand that repeated multiplication can be written more efficiently
- Recall multiplication facts up to at least
- Know that some numbers can be arranged into equal rows and columns
- Be familiar with Use arrays or factor pairs to represent multiplication
Worked Examples
Worked Example 1
Decide whether each number is prime or composite:
a)
b)
c)
Worked Example 2
Write the meaning of each term and Evaluate where possible:
a)
b)
c)
Worked Example 3
Find the highest common factor of:
a)
b)
Worked Example 4
Find the lowest common multiple of:
a)
b)
Worked Example 5
Find each value:
a)
b)
c)
Worked Example 6
Find each value:
a)
b)
c)
Problems
Problem 1
Decide whether each number is prime or composite:
a)
b)
c)
Problem 2
Write the meaning of each term and evaluate where possible:
a)
b)
c)
Problem 3
Find the highest common factor of:
a)
b)
Problem 4
Find the lowest common multiple of:
a)
b)
Problem 5
Find each value:
a)
b)
c)
Problem 6
Find each value:
a)
b)
c)
Exercises
Understanding and Fluency
Exercise 1.
Decide whether each number is prime or composite:
a)
b)
c)
d)
Exercise 2.
List all the factors of each number, then decide whether it is prime or composite:
a)
b)
c)
Exercise 3.
Find the highest common factor of each pair of numbers:
a)
b)
c)
Exercise 4.
Find the lowest common multiple of each pair of numbers:
a)
b)
c)
Exercise 5.
Find each square or square root:
a)
b)
c)
d)
Exercise 6.
Find each cube or cube root:
a)
b)
c)
d)
Exercise 7.
Complete the table:
a) square of
b) square root of
c) cube of
d) cube root of
Exercise 8.
Find both the HCF and the LCM of each pair:
a)
b)
c)
Reasoning
Exercise 9.
Explain why
Exercise 10.
Sofia says that
Exercise 11.
Which is greater, the HCF or the LCM of
Exercise 12.
Explain why
Exercise 13.
A student says that
Problem-solving
Exercise 14.
Two lights flash every
Exercise 15.
Two classes are making equal groups for a sports activity. One class has
Exercise 16.
A square garden has side length
Exercise 17.
A cube-shaped box has side length
Exercise 18.
Two buses leave a station every
Exercise 19.
A number is composite, has a square root that is a whole number, and is less than
Potential Misunderstandings
- Students may think a prime number is any odd number
- Students may think
is prime because it has only one factor - Students may forget that a prime number must have exactly two factors, not fewer and not more
- Students may confuse factors with multiples
- Students may think the highest common factor is always the larger of the two numbers
- Students may think the lowest common multiple must be one of the original numbers
- Students may confuse square with doubling
- Students may think
means instead of - Students may confuse square root with dividing by
- Students may confuse cube with multiplying by
- Students may think cube root means divide by
- Students may mix up the notation
and - Students may not Recognise that square roots and cube roots here are only whole numbers for certain values