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## Factors, Multiples, Prime Factors HCF’s and LCM’s

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**Factors, Multiples,**Prime Factors HCF’s and LCM’s**What do the following words mean?**A number in another numbers times table MULTIPLE Multiples of 6 are: 6, 12, 18, 24, 30, ... A number that divides exactly into another FACTOR Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 A number that has EXACTLY 2 factors, 1 and itself PRIME 7 is prime because it has only 2 factors, 1 and 7 A number that is found by multiplying a number by itself SQUARE 64 is square because it is 8 x 8 A number that is found by multiplying a number by itself and by itself again. CUBE 27 is cube because 3x3x3 = 27**Shade all the prime numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Shade all the prime numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Shade all the square numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Shade all the square numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Shade all the cube numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Shade all the cube numbers between 1 and 130**Discuss these with your neighbour to make sure you agree**Factors and multiples game**First player chooses an EVEN number LESS THAN 50 and crosses it out. The second player chooses a number that is either a FACTOR or a MULTIPLE of the first number to cross out. The players continue in turn crossing out a factor or multiple of the previous number. The loser is the first person that is UNABLE to cross a number out.**Factors and multiples puzzle**Place these 10 headings cards around the grid. Place these 25 numbers inside the grid.**What is a PRIME NUMBER?**It is a number which has EXACTLY 2 factors – 1 and itself Write down the first 20 prime numbers… 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71**400**Write 400 as a product of primes… 2 200 400 = 2 x 2 x 2 x 2 x 5 x 5 = 24 x 52 2 100 2 50 2 25 5 5**360**Write 360 as a product of primes… 2 180 360 = 2 x 2 x 2 x 3 x 3 x 5 = 23 x 32 x 5 2 90 2 45 15 3 3 5**Write the following numbers as products of prime factors:**(a) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28 (b) 500 = 2 x 2 x 5 x 5 x 5 = 22 x 53 (c) 1125 = 3 x 3 x 5 x 5 x 5 = 32 x 53 = 2 x 2 x 3 x 3 x 5 x 7 = 22 x 32 x 5 x 7 (d) 1260 = 2 x 2 x 2 x 2 x 5 x 7 x 11 = 24 x 5 x 7 x 11 (e) 6160**Use the product of prime factors of 360 and 400 to find**the Highest Common Factor (HCF) and the Lowest Common Multiple of (LCM). Explain what these two answers mean. 400 = 2 x 2 x 2 x 2 x 5 x 5 360 = 2 x 2 x 2 x 3 x 3 x 5 400 = 2 x 2 x 2 x 2 x 5 x 5 360 = 2 x 2 x 2 x 3 x 3 x 5**400 =**2 x 2 x 2 x 2 x 5 x 5 360 = 2 x 2 x 2 x 3 x 3 x 5 HCF = 2 x 2 x 2 x 5 = 40 400 = 2 x 2 x 2 x 2 x 5 x 5 360 = 2 x 2 x 2 x 3 x 3 x 5 LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 3600 HCF = Biggest number that is a factor of 400 AND 360 LCM = Smallest number that is a multiple of 400 AND 360**Use the product of prime factors of 1260 and 6160 to find**The HCF and LCM of 1260 and 6160. 1260 = 2 x 2 x 3 x 3 x 5 x 7 6160 = 2 x 2 x 2 x 2 x 5 x 7 x 11 x 5 x 7 HCF = 2 x 2 = 140 1260 = 2 x 2 x 3 x 3 x 5 x 7 6160 = 2 x 2 x 2 x 2 x 5 x 7 x 11 LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 11 = 55440