Splitting the number Numbers, like everything else, can be split up into smaller parts. For atoms, these smaller parts are called quarks. For numbers, they are called: _ _ _ _ _ _ _ F A C T O R S

The Horseshoe Method 30 1 2 3 5 6 10 15 30 1 x 30 2 x 15 3 x 10 5 x 6

Divisibility How can we tell if a number divides by 2? Can you come up with any rules for the other numbers?

Divisibility Rules 2: The last digit is even (0, 2, 4, 6, 8) 3: Digits add up to a multiple of 3 4: The last 2 digits make a multiple of 4 5: The last digit is 0 or 5 6: The number divides by 2 and 3 7: (Nothing easy – sorry! Just try dividing) 8: The last 3 digits make a multiple of 8 9: Digits add up to a multiple of 9 10: The last digit is 0

Some numbers cannot be broken down at all These are called: _ _ _ _ _ numbers Eg: 17 = 1 x 17. (No other factors) Find the first 7 prime numbers. (prime numbers have exactly 2 factors, so 1 is not a prime, but 2 is a prime) P R I M E 2 3 5 7 11 13 17

12 18 Every number can be broken down until it is just prime numbers multiplied together. 3 4 6 3 2 2 2 3 2 x 2 x 3 2 x 3 x 3

Does it divide by 10? By 5? By 2? By 3? If none, check 7, 11, ... Otherwise, prime. 420 = 22×3×5×7 10 42 2 21 5 2 7 3

Use the factor tree method to break down these numbers into their smallest parts (‘prime factors’) 28 100 48 32 68 19 45 5050 891

581202 444444 510 54321 98172635400 67

12 18 3 4 6 3 2 2 2 3 2 x 2 x 3 2 x 3 x 3

12 12 3 HCF: 2 x 3 = 6 2 2 2 3 3 18 18 = x x x x = 2 x 2 x 3 2 x 3 x 3 LCM: 2 x 2 x 3 x 3 = 36

50 70 5 10 10 7 2 5 2 5 2 x 5 x 5 2 x 5 x 7

50 50 70 70 HCF: 2 x 5 = 10 5 2 2 5 5 7 = x x x x = 2 x 5 x 7 2 x 5 x 5 LCM: 2 x 5 x 5 x 7= 350