What is the greatest possible length of scale to measure exactly the following?
15 feet, 12 feet 9 inches, 16 feet 3 inches, and 23 feet 6 inches
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 3 inches.
To find the greatest possible length of the scale, we need to find the highest common factor (HCF) of all the given lengths in feet and inches.
First, let's convert all lengths to inches:
15 feet = 180 inches
12 feet, 9 inches = 153 inches
16 feet, 3 inches = 195 inches
23 feet, 6 inches = 282 inches
Now, we can find the HCF of these lengths by prime factorizing each number and finding the common factors:
⇒ 180 = 22 × 32 × 5
⇒ 153 = 32 × 17
⇒ 195 = 3 × 5 × 13
⇒ 282 = 2 × 3 × 47
The common factors are 3, so the HCF is 3 inches.