(Abstract Algebra 1) Relatively Prime Integers
(Abstract Algebra 1) Relatively Prime Integers

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Prime Factorization Prime factorization is the long string of factors that is made up of all prime numbers.

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Factor Tree A factor tree is a way to organize and help you determine the prime factorization of a number. Factor trees use branches to show how a number is broken down into prime numbers.

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A power consists of two elements: the base and the exponent.

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Base In an exponent expression, the base is the factor that is repeatedly multiplied.

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Exponent The exponent of a power is the number of times the base is used as a factor of repeated multiplication.

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Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic states that every natural number is either prime or can be written as a unique product of primes.

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Common Multiple A common multiple is a number that is a multiple of two or more numbers. Example: multiples of 60: 60, 120, 180, 240, 300, 360, 420, multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, some common multiples of 60 and 24: 120,

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Least Common Multiple (LCM)
The least common multiple, or LCM, is the smallest multiple (other than zero) that two or more numbers have in common. Example: multiples of 60: 60, 120, 180, 240, 300, 360, 420, multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, some common multiples of 60 and 24: 120, least common multiple of 60 and 24: 120

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A common factor is a number that is a factor of two or more numbers.
Example: factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 common factors of 60 and 24: 1, 2, 3, 4, 6, and 12

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Greatest Common Factor (GCF)
The greatest common factor, or GCF, is the largest factor two or more numbers have in common. Example: factors of 16: 1, 2, 4, 8, 16 factors of 12: 1, 2, 3, 4, 6, 12 common factors: 1, 2, 4 greatest common factor: 4

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Relatively Prime Numbers
Two numbers that do not have any common factors other than 1 are called relatively prime numbers. Examples: Positive whole number pairs that have a difference of 1 (4 and 5, 10 and 11, 15 and 16) are always relatively prime numbers.

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Word definition

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