What is the greatest common factor of 32 and 45?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 32 and 45. The GCF is the largest number that divides both 32 and 45 without leaving a remainder.
Answer
1
Answer for screen readers
The greatest common factor (GCF) of 32 and 45 is 1.
Steps to Solve
- Find the prime factorization of 32
We start by breaking down the number 32 into its prime factors.
The prime factorization of 32 is: $$ 32 = 2^5 $$
- Find the prime factorization of 45
Next, we break down the number 45 into its prime factors.
The prime factorization of 45 is: $$ 45 = 3^2 \times 5 $$
- Identify common factors
Now we look for any common prime factors in the factorizations of 32 and 45.
Factors of 32: $2^5$
Factors of 45: $3^2 \times 5$
There are no common prime factors between 32 and 45.
- Determine the GCF
Since there are no common prime factors, the greatest common factor (GCF) is 1.
Therefore, the GCF of 32 and 45 is: $$ \text{GCF}(32, 45) = 1 $$
The greatest common factor (GCF) of 32 and 45 is 1.
More Information
The GCF represents the largest number that can exactly divide two numbers without a remainder. In the case of 32 and 45, since they have no common factors, the GCF is the smallest possible value, which is 1.
Tips
A common mistake is to confuse the GCF with the least common multiple (LCM). It’s important to remember that the GCF is the largest factor common to both numbers, while the LCM is the smallest multiple common to both.
