Examkin

Question

Difficulty: EasyFactors, Multiples, and Primes

A carpenter has two pieces of wood. One piece is 1818 inches long and the other is 2424 inches long. She wants to cut both pieces into smaller segments of equal length with no wood left over. What is the greatest possible length, in inches, of each segment?

  1. A
    3
  2. 6Answer
  3. C
    42
  4. D
    72

Answer

The greatest possible length of each segment is 6 inches.
To find the greatest possible length for the cut segments, we must find the greatest common factor (GCF) of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest number appearing in both lists is 6, making it the correct answer.

Step-by-Step Solution

1
Identify the goal of the problem.
We need to divide both 18 and 24 into equal segments of the maximum possible length. This means finding the Greatest Common Factor (GCF) of 18 and 24.
The phrase 'cut into equal length' implies finding a common factor, and 'greatest possible length' specifies the GCF.
2
List the factors of 18.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
These are all the integers that divide evenly into 18.
3
List the factors of 24.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
These are all the integers that divide evenly into 24.
4
Identify the greatest factor common to both lists.
The common factors are 1, 2, 3, and 6. The greatest among these is 6.
This is the largest segment size that will evenly divide both pieces of wood.

Key Concept

The Greatest Common Factor (GCF) is the largest positive integer that divides evenly into two or more given numbers. It is commonly used when splitting items into equal, maximum-sized groups.
Estimated Time:1m 0s
Rate this question

Topics

Factors, Multiples, and Primes

More questions from this topic