GMAT Math : Arithmetic
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Example Questions
Example Question #51 : Understanding The Properties Of Integers
What is the greatest common factor of 
Firstly, we should start by noticing that 
Example Question #221 : Arithmetic
What is the greatest common factor of 
To find the greatest common factor of two numbers, we must first write their respective prime factorization, in other words, we must write these numbers as a product of prime numbers. This can be done by firstly dividing a given number by 2, then 3, and all the way up to higher prime numbers.
Then we simply have to multiply all the common factors, with their lowest power:
The common factors here are only 5's, and the lowest power of 5 in both numbers is 
Example Question #57 : Understanding The Properties Of Integers
What is the greatest common factor of 
We start by writing the prime factorization of these two numbers: 
Note that to find the prime factorization there is not much to do other than just starting with the smallest prime numbers and the GMAT requires to know the prime numbers under 100.
The common factors are only 2's, and we apply to this common factor of the lowest power, which is 1. Therefore, the final answer is 
Example Question #58 : Understanding The Properties Of Integers
What is the greatest common factor of 
We start by writing the prime factorization of these two numbers:
By taking the common factors and raising them to the lowest power, we get 
Example Question #1771 : Problem Solving Questions
What is the least common multiple of 
For the least common multiple, we also need to write out the prime factorization of these numbers, as follows:
Then, we multiply all the factors raised to their highest powers.
Here we have: 
Example Question #222 : Arithmetic
What is the least common multiple of 
We begin by writing the prime factorization of 78 and 36.
The rule to find the least common multiple is to multiply all factors raised to their highest power.
Here we have: 
Example Question #222 : Arithmetic
What is the least common multiple of 
Let's start by writing the prime factorization of these two numbers:
Then we just have to multiply each factor raised to its highet power for common factors, as follows:
Example Question #1773 : Problem Solving Questions
You know that 
For any positive integer 
Therefore,
Example Question #61 : Understanding The Properties Of Integers
We can use the property that for 
Therefore,
Example Question #225 : Arithmetic
Using the property
Notice that the GCD or greatest common divisor is the same thing as the GCF, or greatest common factor.
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