Be My Factor!
18 and 6: a factor and a multiple that belong together.
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6 is a factor of 18, so 18 is a multiple of 6, and their HCF is 6.
Turn examples into rules that always hold, such as 'if one number divides the other, it is their HCF', and write them with algebra.
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If one number is a factor of the other, it is their HCF.
The HCF of 6 and 18 is 6, one of the two numbers. When does that happen?
Exactly when one number is a factor of the other, so the other is a multiple of it.
18 and 6: a factor and a multiple that belong together.
6 is a factor of 18, so 18 is a multiple of 6, and their HCF is 6.
If m is one number and also the HCF, what can the other number be?
Problem. For pairs where one number is the HCF: (a) if is a number, what could the other be? (b) if is a number, what could the other be? (Textbook p. 59)
Find such pairs and describe them with algebra.
Figure it Out, Textbook p. 59, Q2. The LCM of 3 and 24 is 24, one of the two numbers.
(a) Find more such pairs. (b) Make a general statement about such numbers, and describe them using algebra.
Check each LCM.
When does this happen? Say it in words.
Use n and a whole number k.
How to make and check a general statement about HCF or LCM.
Why two consecutive numbers always have HCF 1 and LCM equal to their product.
Problem. What can you say about the HCF and LCM of two consecutive numbers?
State and explain rules for HCF and LCM of special pairs.
Figure it Out, Textbook p. 59, Q1 and Q3. For each, try examples, write a general statement, and give a reason.
HCF of: (a) two consecutive even numbers (b) two consecutive odd numbers (c) two even numbers (d) two consecutive numbers (e) two co-prime numbers
LCM of: (a) two multiples of 3 (b) two consecutive even numbers (c) two consecutive numbers (d) two co-prime numbers
Example + statement + reason for each.
Example + statement + reason for each.
Example + statement + reason for each.
Example + statement + reason for each.