Mathematical Reasoning Chapter 5 Vocab

Number Theory

the study of the properties of the natural or
counting numbers.

Divisibility

one counting number is divisible by another if dividing the
first by the second leaves a remainder of zero.

Even

a natural number divisible by 2.

Odd

a natural number written in the form 2k – 1.

Factor/divisor

when natural number a is divisible by natural number b

Multiple

the result you get when you multiply a given number by a
whole number or an integer.

Factorization

rewriting a number as a product of factors.

Prime Number

a natural number greater than 1 that has only 1 and
itself as factors.

Composite Number

a natural number greater than 1 that is not prime

Prime Factorization

when a natural number is expressed as a product
of prime numbers

Perfect Number

a natural number equal to the sum of its proper
divisors.

Proper Divisors

include all divisors of a number but the number itself

Conjecture

an educated guess or unproven statement that is believed
to be true based on observations, patterns, or limited evidence.

Deficient Number

a natural number that is less than the sum of its
proper divisors.

Abundant Number

a natural number that is greater than the sum of
its proper divisors.

Amicable/friendly numbers

natural numbers a & b where the sum of
the proper divisors of a is b and the sum of the proper divisors of b is a

Twin Primes

primes that differ by two

Pythagorean Theorem

𝑎2 + 𝑏2 = 𝑐2

Greatest Common Factor

the greatest natural number that is a
factor of all the numbers in the group

Least Common multiple

the least natural number that is a multiple of
all numbers in the group.