# GRE® Number Properties

#### Concepts Tested in Number Properties, Number Sytems, and Number Theory

One can expect three to five questions from number properties, number system, and number theory in the quant section of the GRE General Test. The concepts are core concepts and you need to get an in depth understanding of these concepts to ace these questions in the GRE quant section. For instance, it is not only sufficient that you know how to find the LCM and HCF of numbers, but you also need to know what is the idea behind finding LCM and in what cases do we find LCM. The following concepts are tested in Number Theory in the GRE test.

• Operations on numbers. Results of operations on odd and even numbers.
• Prime numbers - how to determine whether a number is prime. Composite numbers. Co prime numbers. Prime factorizing a number.
• Properties of squares of numbers, cubes of numbers.
• LCM and HCF of numbers. When to find the LCM or HCF. LCM and HCF of fractions.
• Remainders, remainders of division of the product and sum of numbers by the same divisor.
• Factorials, number of trailing zeroes.
• Finding units digit of numbers. Finding tens digit of numbers

1. N is the smallest positive integer that has 7 factors.

Column A Column B
Number of factors of √N Number of factors of (N - 2)
1. Column A is greater
2. Column B is greater
3. The two columns are equal
4. Cannot be determined
Approach to solve this GRE Number Properties QC question

Step 1: Find the interger N
Step 2: Evaluate Column A. Compute the number of factors of √N
Step 3: Evaluate Column B. Compute the number of factors of (N - 2)
Step 4: Compare values in step 2 and step 3 to find the answer to this GRE quantitative comparison question

2. How many pairs of natural numbers exist whose HCF is 12 and add up to 216?

1. 6
2. 3
3. 9
4. 18
5. 17
Approach to solve this Number Properties question

Step 1: The two numbers can be written in the form 12x + 12y = 216, where x and y are positive integers and coprime to each other
Step 2: So, x + y = 18. List possible values of x and y that are co prime to each other and add up to 18

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