Download Factors - Wey Valley School

The Wey Valley School & Sports College
Mathematics Home Study
Page 1
FACTORS & MULTIPLES
1. Look at the numbers in the circle.
UNIT: Factors
Support work: Question 1 on each page
Core work: Question 2 on each page
Extension work: Question 3 on each page
(a)
(b)
(c)
(d)
Which numbers are odd?
Which numbers divide by 5?
Which numbers divide by 3?
Which numbers are multiples of 2?
2. (a) List all the factors of
HELP!
The factors of a number are the numbers which divide into it
exactly e.g. the factors of 12 are 1, 2, 3, 4, 6 & 12.
(i) 20
(ii) 30
(iii) 40.
(b) Use your answers to (a) to find the highest common factor
(hcf) of (i) 20 & 30 (ii) 30 & 40 (iii) 20, 30 & 40
(c) Write down the first 8 multiples of (i) 4 (ii) 6
The multiples of a number are the numbers it divides into exactly
(the times table for the number) e.g. the multiples of 4 are 4, 8,
12, 16, 20, 24, …. There are infinite multiples for every number.
(d) Use your answers to (b) to find the lowest common
multiple (lcm) of 4 and 6.
A prime number is a number that has only two factors: 1 & itself.
The first few prime numbers are 2, 3, 5, 7, 11, …
3. (a) Find all the common factors of these pairs of numbers:
On Page 3 the word “calculate” is used, this does not always
mean ‘use a calculator’. It does mean work out the answer to the
sum as a number. It is good practice to do what you can without
a calculator and then use a calculator to check the answers that
you get.
Page 2
(i) 77, 88
(ii) 28, 16
(iii) 48, 40
(iv) 14, 22
(v) 63, 49
(b) Find all the numbers which are less than 50 and are
common multiples of these pairs of numbers:
(i) 3, 7
(ii) 10, 15
(iii) 2, 3
(iv) 14, 4
(v) 8, 10
Page 3
PRIME NUMBERS & FACTOR TREES
1. (a) Write down which numbers in the
circle are prime.
(b) List all the factors of 50.
Which of these factors are prime
numbers?
2. (a) Copy and complete the factor tree for 84:
INDEX NOTATION
1. (a) Copy the following statements and fill in the missing
numbers:
(i) 6 × 6 × 6 × 6 = 6
(ii) 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 7 
(iii) 2 × 2 × 2 × 2 × 2 = 2
(iv) 10 × 10 × 10 × 10 × 10 × 10 = 10 
(b) Write out the following in full: (i) 3 4 (ii) 57
(iii) 82
2. (a) Write down the squares of these numbers:
(i) 8 (ii) 12 (iii) 7 (iv) 1 (v) 9
(b) Draw 2 different factor trees for 30.
(c) List the factors of 80.
How many of the factors of 80 are prime numbers?
3. (a) Explain why 51 is not a prime number.
(b) Using the factor tree in question 2 (a), copy & complete the
statement below to write 84 as the ‘product of its prime
factors’:
84 = 2× 3 × 7
(c) By drawing factor trees, or otherwise, write each of the
following numbers as a product of its prime factors:
(i) 92
(ii) 48
(iii) 400
(iv) 1008
(b) Calculate:
(i) 62 (ii) 104
(iii) 25
(iv) 33
(v) 42
(vi) 113
3. (a) Write down the square roots of these numbers:
(i) 36 (ii) 4 (iii) 121 (iv) 25 (v) 100
(b) Write down the cubes of these numbers:
(i) 4 (ii) 1 (iii) 10
(c) Copy each statement and fill in the missing number:
(i) 1000 = 3 (ii) 81 = 3 (iii) 12 = 144
(iv) 16 = 2 (v) 625 = 5 (vi) 1000000 = 10
(d) Calculate:
(i) 23 × 102
(ii) 103 × 32
(iii) 107 × 25