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### Concepts Tested in Number Properties, Number Sytem & Number Theory

One can expect three to five questions from number properties, number system and number theory in the GRE. 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.
- Factors, number of factors, sum of factors, product of factors, ways of expressing a number as a product of its factors.
- 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

N is the smallest positive integer that has 7 factors.

Quantity A Quantity B Number of factors of \\sqrt{N}). Number of factors of (N-2). - Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

How many pairs of natural numbers whose HCF is 12 add up to 216?

- 6
- 3
- 9
- 18
- 17