What is the greatest integer that is a factor of all of the given integers?
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To find the greatest integer that is a factor of all the given integers, we need to identify the common factors of the integers and then choose the largest one.
Here are the steps to find the greatest integer factor:
1. Write down the prime factorization of each integer. Prime factorization involves breaking down each integer into its prime factors.
2. Identify the common prime factors among all the integers. These are the prime factors that appear in the factorizations of all the given integers.
3. Multiply the common prime factors to get the greatest integer that is a factor of all the given integers.
Let's take an example to illustrate the process. Suppose we have the integers 12, 18, and 24.
1. Prime factorization of 12: 12 = 2^2 * 3
Prime factorization of 18: 18 = 2 * 3^2
Prime factorization of 24: 24 = 2^3 * 3
2. Common prime factors: Among the given integers, the common prime factors are 2 and 3.
3. Multiply the common prime factors: The greatest integer factor is obtained by multiplying the common prime factors, which gives us 2 * 3 = 6.
Therefore, the greatest integer that is a factor of all the given integers (12, 18, and 24) is 6.
To find the greatest integer that is a factor of all the given integers, you need to find the common factors of those integers and determine the largest among them.
Here's how you can do it step by step:
1. Make a list of all the given integers.
2. Find the factors of each integer in the list. A factor of an integer is any number that divides it without leaving a remainder.
3. Identify the common factors among all the integers. These are the factors that appear in the factor list of every integer.
4. Find the largest common factor among the identified factors. This will be the greatest integer that is a factor of all the given integers.
For example, let's say we have the integers 24, 36, and 48.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 3, 4, 6, 12
Among the common factors, the largest one is 12. Therefore, 12 is the greatest integer that is a factor of 24, 36, and 48.
In general, you can follow these steps to find the greatest integer that is a factor of any given set of integers.