Name a pair of numbers whose greatest common factor is the same as one of the numbers.
Pick any number x
Then any number y which is a multiple of x
will have GCF(x,y) = x
To find a pair of numbers whose greatest common factor (GCF) is the same as one of the numbers, we need to look for numbers that have a factor in common. One such example would be a pair of identical prime numbers.
Let's take the number 7 as an example. If we choose another number that is also 7, then the GCF of these two numbers will be 7. So, a pair of numbers that fit the criteria is (7, 7).
In this case, both numbers are the same, and their GCF is equal to one of the numbers which is 7.
To find a pair of numbers whose greatest common factor (GCF) is the same as one of the numbers, we need to consider the property that every number is a factor of itself.
So, let's consider two scenarios:
1. When the GCF is the first number:
In this case, we can choose any number and pair it with itself. For example, let's choose 5. So, a pair of numbers whose GCF is the same as the first number would be (5, 5).
2. When the GCF is the second number:
In this case, we need to choose a prime number where the second number is a multiple of that prime number. Let's consider the prime number 7. We can pair it with any multiple of 7, such as 7 x 2 = 14. So, a pair of numbers whose GCF is the same as the second number would be (7, 14).
To summarize:
- Pair 1: (5, 5)
- Pair 2: (7, 14)