NUMBER THEORY

The set of numbers 1, 2, 3, 4, 5, and so on, used for counting.

What are natural numbers?

The set of natural numbers plus zero.

What are whole numbers?

The set of whole numbers plus their negative counterparts.

What are integers?

A number that can be written as a fraction of two integers.

What is a rational number?

A number whose decimal form never ends and never repeats.

What is an irrational number?

The set combining all rational and irrational numbers.

What is the set of real numbers?

The only even prime number.

What is 2?

A number with exactly two factors, 1 and itself.

What is a prime number?

A number with more than two factors.

What is a composite number?

This number is neither prime nor composite.

What is 1?

Zero is classified this way in terms of being prime or composite.

What is neither prime nor composite?

The divisibility rule for 3 involves doing this to the digits.

What is adding them up (checking if the sum is divisible by 3)?

The divisibility rule for 9 involves doing this to the digits.

What is adding them up (checking if the sum is divisible by 9)?

A number ending in 0 or 5 is divisible by this.

What is 5?

A number is divisible by 4 if this part of the number is divisible by 4.

What are the last two digits?

A number is divisible by 8 if this part of the number is divisible by 8.

What are the last three digits?

The rule for checking divisibility by 7: double this digit and subtract it from the rest.

What is the last digit?

The process of breaking a number into the primes that multiply to form it.

What is prime factorization?

The prime factorization of 60.

What is 2 squared times 3 times 5?

The prime factorization of 100.

What is 2 squared times 5 squared?

The largest number that divides evenly into two or more numbers.

What is the Greatest Common Factor (GCF)?

The smallest number that two or more numbers divide into evenly.

What is the Least Common Multiple (LCM)?

The GCF of 18 and 24.

What is 6?

The LCM of 18 and 24.

What is 72?

The LCM of 4 and 6.

What is 12?

The relationship connecting GCF, LCM, and the product of two numbers.

What is GCF times LCM equals the product of the two numbers?

Two numbers whose GCF is 1 are described this way.

What are relatively prime (or coprime)?

A number that equals the sum of its factors, excluding itself.

What is a perfect number?

The smallest perfect number.

What is 6?

The second smallest perfect number.

What is 28?

A number whose factors (excluding itself) add up to less than the number.

What is a deficient number?

A number whose factors (excluding itself) add up to more than the number.

What is an abundant number?

Prime numbers that differ by exactly 2, such as 11 and 13.

What are twin primes?

The unsolved conjecture stating every even number greater than 2 is the sum of two primes.

What is the Goldbach Conjecture?

A sequence where the same value is added each time.

What is an arithmetic sequence?

A sequence where the same value is multiplied each time.

What is a geometric sequence?

A sequence where each number is the sum of the two before it, starting 1, 1, 2, 3, 5, 8.

What is the Fibonacci sequence?

A number produced by multiplying an integer by itself.

What is a perfect square?

A number produced by multiplying an integer by itself three times.

What is a perfect cube?

The square root of 49.

What is 7?

The cube root of 27.

What is 3?

Numbers formed by adding consecutive counting numbers, such as 1, 3, 6, 10, 15.

What are triangular numbers?

The distance of a number from zero on a number line, always non-negative.

What is absolute value?

A number that reads the same forwards and backwards, such as 121 or 1331.

What is a palindrome number?

The product of all positive integers up to a given number, symbolized by an exclamation point.

What is a factorial?

5 factorial (5!).

What is 120?

The numeral system using letters like I, V, X, L, C, D, and M.

What are Roman numerals?

The Roman numeral representation of 40.

What is XL?

The Roman numeral representation of 1994.

What is MCMXCIV?

A way of writing very large or very small numbers using powers of 10.

What is scientific notation?

5,300,000 written in scientific notation.

What is 5.3 times 10 to the 6th power?

Any number (except 0) raised to the power of 0 equals this.

What is 1?

The result of multiplying two negative numbers together.

What is a positive number?

The sum of the digits of a number, repeatedly added until a single digit remains.

What is the digital root?