Introduction to Criterion B, C
Investigations to Choose
Choose one of the following questions to investigate and find patterns.
1) HCF of Sums
1) HCF of Sums
- Choose any three different digits from 1 to 9. Write down the six possible two digit numbers that can be formed using these digits. For example, if we choose the digits 2, 7 and 8, we would write down: 27, 28, 72, 78, 82, 87 which add to 374. Find the sum of the six numbers and write their sum in prime factored form. Record your results in a table:
- Choose another 3 and repeat the steps above
- Choose another 2 and repeat the steps above
- Find the HCF of all the sums (3rd column)
- What is the pattern you see with all possible choices of 3 different digits
- Hint: Any two digit number with digits a and b has the form 10a + b. For example, 37 = 10(3) + 7
2) Multiples
Charlie said: "Alison, think of a two-digit number. Reverse the digits and add your answer to your original number. What is it divisible by."
Alison chose 42, added 24 and got the answer 66: "It is divisible by 1,2,3, 6,11, 22, 33, 66?"
Charlie said: "Do it again with different numbers and see if there is one number that is the same."
- Try the way 2 more times to see if it is correct. Find the greatest common factor of the three numbers.
- Prove why this is always true.
- Hint: A two-digit number ab, where a represents the number in the tens column, and b respresents the number in the units. This can be written as 10a+b
Unit 1: Book Review
Review Set 1A and 1B