LCM and GCD – Divisibility Rules & Prime Factorization (Vocabulary)

Vocabulary flashcards covering LCM, GCD/GCF, divisibility rules, and prime factorization concepts as discussed in the lecture notes.

LCM (Least Common Multiple)

The smallest positive integer that is a multiple of two or more given numbers.

GCD (Greatest Common Divisor) / GCF (Greatest Common Factor)

The largest positive integer that divides two or more numbers without a remainder.

Divisibility Rule

A shortcut test to determine whether a number is divisible by another number without performing full division.

Prime Factorization

Expressing a number as a product of prime factors (e.g., 56 = 2^3 × 7).

Factor Tree

A visual method to break a number down into its prime factors by repeatedly factoring.

Factor

A number that divides another number exactly (no remainder).

Multiple

A product of a number and a positive integer; numbers that the original number goes into.

Prime Number

A natural number greater than 1 with exactly two distinct positive divisors: 1 and itself.

Composite Number

A natural number greater than 1 that has more than two distinct positive divisors.

Natural Numbers

Positive counting numbers: 1, 2, 3, 4, …

Integers

All positive and negative whole numbers, including zero.

Rational Numbers

Numbers that can be written as a ratio of two integers (a/b) with b ≠ 0.

Irrational Numbers

Numbers that cannot be written as a ratio of two integers; their decimal expansions do not terminate or repeat (e.g., π, √2).

Real Numbers

All rational and irrational numbers on the number line.

Imaginary / Complex Numbers

Imaginary numbers involve i = √-1; complex numbers have the form a + bi, combining real and imaginary parts.

One is Neither Prime nor Composite

The number 1 has only one positive divisor, so it is neither prime nor composite.

Divisible

A number A is divisible by B if A ÷ B yields a remainder of 0 (no remainder).

Overlapping Primes (for GCF)

When finding the GCF, multiply the common prime factors from the prime factorizations (using the smallest powers shared).

Prime Factorization of 56

56 = 2^3 × 7, i.e., the product of prime factors of 56.