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Maths Revision: Finding Factors
Factors are whole numbers that divide exactly into another number. This means that if you divide a number by the factor, there will be no remainders. The answer is also a factor. Product ÷ factor 1 = factor 2 16 ÷ 1 = 16 ( so 1 and 16 are a factor pair)
In class, we found factors by listing factor pairs. Most factors come in pairs, unless the product is a square number. E.g. Find all factors of 16 1 , 16 2 , 8 4
Work in a systematic order starting with 1 x
Use your multiples facts to identify factors. E.g. all even numbers must have 2 as a factor.
Finding Common Factors To find the common factors of numbers, list the factors for each product. Once you have done this, circle any factors that appear in both lists.
16 1 , 16 2 , 8 4
The circled factors are called the common factors. The largest factor that is circled is called the highest common factor.
4 does not have a pair because 16 ÷ 4 = 4 so the pair would be 4 , 4 but we don’t need to write it down twice. This means that 16 is a square number as it’s the product of 16^2_._
Maths Revision: Multiples
A multiple is the product (the answer you get) of 2 whole numbers multiplied together. For example, a multiple of 2 is any number that will appear in the 2 x table. To find multiples of 2, you need to multiply any whole number by 2.
Multiples of 2: end in 0,2,4,6 or 8. Multiples of 3: have a digital sum of 3,6 or 9. e.g. 3072—3+0+7+2 = 12 then 1+2= 3 so this is a multiple of 3. Multiples of 4: the last 2 digits will be in the 4x table e.g. 7840 – 40 is in the 4x table. Multiples of 5: end in 5 or 0. Multiples of 10: end in a 0.
Multiple Rules to Remember Finding Common Multiples List the multiples of each whole number. Once you have done this, circle any product that appears in all lists. 8 8 16 24 32 40 48
20 40 60 80 100 120
10 20 30 40 50 60 The circled products are common multiples. The smallest multiple circled is the lowest common multiple.
Maths Revision: Square Numbers
Maths Revision: Cubed Numbers
A cubed number is the product of multiplying a number by itself 3 times. The symbol for cubed is ( 3 ). E.g. Instead of calculating 3 x 3 x 3, you can say 3^3 (3 cubed). The product is the cubed number.
A square number is the product of a number multiplied by itself. The symbol for squared is ( 2 ). E.g. Instead of saying 4 x 4, you can say 4 2 (4 squared). The product ( answer) is the square number, not the numbers you are multiplying together.
They are called square numbers because the array will form a square.
This array represents 2 x 2 or 2^2. The product is 4 so we know that 4 is a square number.
They are called cubed numbers as the array will create a 3D cube.
This shows 2 x 2 x 2 or 2^3. It is 2x2 (the square) multiplied by
23 = 8 so 8 is a cubed number.
TASK 2: Multiples
A) Colour in the common multiples of four and nine.
B) Give 3 common multiples for each pair of numbers.
3 and 5 4 and 7 5 and 8
C) Colour in the common multiples of six, eight and twelve.
(You may want to use multiple lists to help you)
(You may want to use multiple lists to help you)
The Lowest Common Multiple is ...
The Lowest Common Multiple is ...
D) A machine beeps every 5 minutes. Another machine beeps every 3 minutes. How many times, in an hour,
will both machines beep at the same time? #ProveIt. Summarise your answer using the key words multiple, common, product.
TASK 3: Square and Cubed Numbers
SQUARE NUMBERS 12 1 x 1 1 22 3 x 3 16 52 36 7 x 7 82 9 x 9 100
CUBE NUMBERS 13 1 x 1 x 1 1 2 x 2 x 2 27 43 5 x 5 x 5 63 343 83 9 x 9 x 9 1000
A) Complete the tables. ( You could use short multiplication to help when cubing to break up each calculation
into 2 smaller calculations. E.g. instead of doing 5 x 5 x 5 mentally, I could calculate 5 x 5 = 25 and then do 25 x 5.)
B) Find the missing numbers in each calculation.
A) 7^2 + 4^2 = B) 8^2 + 10^2 = C) 5^3 - 5^2 =
D) 5^2 + = 89 E) - 82 -= 17 F) 3^2 x 2^2 =
G) 3^2 + = 5^2 H) 6^3 ÷ 2^2 = I) 13^2 =
C) The sum of 2 square numbers is 25. What are the 2 squared numbers?
D) The sum of 3 square numbers (less than 144) is another square number. What are the square numbers?
