Answer:
20 cm
Step-by-step explanation:
To find the greatest length of a measuring stick that can measure exactly 40 cm, 60 cm, and 80 cm, we need to find the highest common factor (HCF) of the three lengths.
To find HCF of 40, 60, 80 we first find the prime factors of each number
[tex]40 = 2 \times 20 = 2 \times 2 \times 10 = 2 \times 2 \times 2 \times 5 = 2^3 \cdot 5[/tex]
[tex]60 = 2 \times 30 = 2 \times \2 \times 15 = 2 \times 2 \times 3 \times 5 = 2^2 \cdot 3 \cdot 5[/tex]
[tex]80 = 2 \times 40 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5[/tex]
To find the HCF we look for the common factors among the three factorizations
These are [tex]2^2 $ and 5[/tex]
and multiply them:
[tex]2^2 \cdot 5 = 20[/tex]
So we can use a measuring stick of length 20 cm to measure the three lengths. no other value greater than 20 will evenly divide into the three numbers
