The [b][i]Greatest Common Factor[/i][/b] of two positive integers [i][color=#0000ff]a [/color][/i]and [i][color=#ff0000]b[/color]:[br]- [/i]is denoted as[i] [b]GCF[/b][/i][b]([i]a, b[/i])[/b][br]- is the largest positive integer among the common divisors of [i][color=#0000ff]a[/color][/i] and[color=#ff0000] [i]b[/i][/color][br]- is always a number smaller than or equal to the smallest number between [i][color=#0000ff]a[/color][/i] and [i][color=#ff0000]b[/color][/i][br][br]To [b]find[/b] the [i][b]GCF[/b][/i] of two positive integers [i][color=#0000ff]a [/color][/i]and [i][color=#ff0000]b[/color][/i]:[br]- write the prime factorization of [i][color=#0000ff]a[/color][/i] and [i][color=#ff0000]b[/color][/i] [br]- [b]multiply [/b]together all the [b]common factors[/b] of the two numbers, [b]each taken once[/b] and with its [b]minimum exponent[/b].
Enter two numbers in the app below, and explore the Euler-Venn representation of their factors and their greatest common factor.
How would you define the colored area of the diagram above, from a sets point of view?
It is the intersection of the set of the divisors of [i]a [/i]and the set of the divisors of [i]b[/i]
Auston Cron edited HCF to GCF to match USA notations. Simona Siva did the hard work.