1. Find the Highest
Common
Factor
15 and 20
15 and 60
12 and 22
12 and 66
39 and 52

2. Co-Prime Investigation
Which of the factors of 120 are coprime (they have a highest common factor of 1)?
When you think you have them all answer these:
Are prime factors always coprime with each other?
What is special about the consecutive factors of 120?
How many times is the number 1 one of the coprime pair?
Select a coprime pair, multiply them together and record the result.
Repeat with a different coprime factor pair of 120.
Do you notice anything about the sum and product of coprime factor pairs?
Start with numbers other than 120. Does the same thing always happen? Convince yourself.
Extension Work underneath
Prime factors are always coprime with each other –Examples: 2 and 3, 2 and 5, 3 and 5.
Consecutive numbers are always coprime – e.g. 1 and 2, 2 and 3, 3 and 4, 4 and 5.
1 is one of the coprime pairs 15 times (1 and another factor is always co-prime). So always number of factors -1

3.
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