Let us find some common factors of the numbers 24 and 36. Note that all jumps in the following questions start from 0.
Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No. 2 is/is not a common factor of 24 and 36.
Yes. 2 is a common factor of 24 and 36. Both 24÷2=12 and 36÷2=18 give whole numbers.
Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No. 3 is/is not a common factor of 24 and 36.
Yes. 3 is a common factor of 24 and 36. Both 24÷3=8 and 36÷3=12 give whole numbers.
Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No. 4 is/is not a common factor of 24 and 36.
Yes. 4 is a common factor of 24 and 36. Both 24÷4=6 and 36÷4=9 give whole numbers.
What other jumps can we take to reach both 24 and 36?
Other jumps that can reach both 24 and 36 are: 6 steps (24÷6=4, 36÷6=6) and 12 steps (24÷12=2, 36÷12=3).
How many common factors can you find for 24 and 36? List them.
The common factors of 24 and 36 are: 1, 2, 3, 4, 6, and 12. There are 6 common factors.
What about jumping by 1 step each time to reach both 24 and 36?
Yes, jumping by 1 step will reach both 24 and 36. The number 1 is always a factor of every number.
Explanation
(a) Since 24 and 36 are both even numbers, they are divisible by 2. Therefore, jumping by 2 steps will reach both positions. (b) 24÷3=8 and 36÷3=12, both giving whole number quotients, so 3 divides both numbers evenly. (c) 24÷4=6 and 36÷4=9, both giving whole number quotients, so 4 divides both numbers evenly. (d) The common factors of 24 and 36 include 6 and 12 as well. 24÷6=4, 36÷6=6, and 24÷12=2, 36÷12=3. (e) Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. Common factors are those appearing in both lists: 1,2,3,4,6,12. (f) The chapter states that 'The number itself and 1 are always factors of any number.' Therefore, 1 is a common factor of all numbers, including 24 and 36.