randRange( 1, 10 ) randRange( 1, 10 ) randRange( 1, 5 ) A_START * FACTOR B_START * FACTOR getGCD( A, B ) getFactors( A ) getFactors( B ) _.intersection( A_FACTORS, B_FACTORS )

What is the greatest common divisor of A and B?

Another way to say this is:

`\gcd(A, B) = {?}`

GCD

The greatest common divisor is the largest number that divides evenly into both `A` and `B`.

Start by thinking about all of the numbers that divide evenly into `A`. In other words, what are the divisors of `A`?

The only divisor of `1` is `1` since that's the only number that divides evenly into `1`:

The divisors of `A` are toSentence( getFactors( A ) ) since those are all the numbers that divide evenly into `A`:

`A \div \color{BLUE}{F} = A/F`

Start by thinking about all of the numbers that divide evenly into `B`. In other words, what are the divisors of `B`?

The only divisor of `1` is `1` since that's the only number that divides evenly into `1`:

The divisors of `B` are toSentence( getFactors( B ) ) since those are all the numbers that divide evenly into `B`:

`B \div \color{GREEN}{F} = B/F`

To find the common divisors, find the all the divisors of `A` and divisors of `B` that are the same.

The only common divisor of `A` and `B` is `GCD` since that's the only number that divides evenly into both `A` and `B`.

The common divisors of `A` and `B` are toSentence( COMMON_FACTORS ) since each of those numbers divides evenly into both `A` and `B`. We're interested in the greatest common divisor.

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The greatest common divisor of `A` and `B` is `GCD`. In other words, `\gcd(A, B) = GCD`.