What is the greatest common factor of 39 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 39 and 42. To solve this, we will find the factors of both numbers and determine the largest factor they share.
Answer
The greatest common factor of 39 and 42 is \(3\).
Answer for screen readers
The greatest common factor of 39 and 42 is (3).
Steps to Solve
- Identify the factors of 39
To find the factors of 39, we can divide 39 by the integers from 1 to 39. The factors of 39 are:
- 1
- 3
- 13
- 39
So, the complete list of factors is: 1, 3, 13, 39.
- Identify the factors of 42
Next, we find the factors of 42 by dividing it by integers from 1 to 42. The factors of 42 are:
- 1
- 2
- 3
- 6
- 7
- 14
- 21
- 42
So, the complete list of factors is: 1, 2, 3, 6, 7, 14, 21, 42.
- Determine the common factors
Now, we find the common factors between the two sets:
- Factors of 39: 1, 3, 13, 39
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The common factors are: 1, 3.
- Identify the greatest common factor
The greatest common factor is the largest number in the list of common factors. Here, that is 3.
The greatest common factor of 39 and 42 is (3).
More Information
The greatest common factor (GCF) is the largest positive integer that divides each of the numbers without leaving a remainder. Knowing the GCF can help simplify fractions and solve problems involving ratios.
Tips
- Not listing all factors: Sometimes students may skip some factors. It’s important to carefully check all possible divisors.
- Confusing GCF with LCM: GCF is different from Least Common Multiple (LCM). Make sure to understand the distinction between the two concepts.
