randRange( 2, 9 ) floor( randRange( B * 2, 100 ) / B ) FACTOR * B getPrimeFactorization( A ) getPrimeFactorization( B ) (function() { var wrongs = []; var i = 2; while( i < 10 ) { if ( A % i !== 0 ) { wrongs.push( i ); } i++; } var shuffled = shuffle( wrongs, 4 ); shuffled.push( B ); return shuffled; })() sortNumbers( WRONGFACTORS )

Which of the following numbers is a factor of A?

`\large{WRONGFACTORS_SORTED.join( "," )}`

`B`

- `wrong`

By definition, a factor of a number will divide evenly into that number. We can start by dividing `A` by each of our answer choices.

`A \div WRONG = floor( A / WRONG )\text{ R }( A % WRONG )`

The only answer choice that divides into `\blue{A}` with no remainder is `\pink{B}`. `\quadFACTOR \times \pink{B} = \blue{A}`.

We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of `B` are contained within the prime factors of `A`.

`A = FACTORIZATION_A.join( "\\times" )\qquad\qquadB = FACTORIZATION_B.join( "\\times" )`

Therefore, `\pink{B}` is a factor of `\blue{A}`.

randRange( 2, 9 ) floor( randRange( B * 2, 100 ) / B ) FACTOR * B getPrimeFactorization( A ) getPrimeFactorization( B ) (function() { var wrongs = []; while( wrongs.length < 4 ) { var i = randRange( 1, 100 ); if ( i % B !== 0 ) { wrongs.push( i ); } } var shuffled = shuffle( wrongs, 4 ); shuffled.push( A ); return shuffled; })() sortNumbers( WRONGMULTIPLES )

Which of the following numbers is a multiple of B?

`\large{WRONGMULTIPLES_SORTED.join( "," )}`

`A`

- `wrong`

The multiples of `B` are `B`, `B*2`, `B*3`, `B*4`...

In general, any number that leaves no remainder when divided by `B` is considered a multiple of `B`.

We can start by dividing each of our answer choices by `B`.

`WRONG \div B = floor( WRONG / B )\text{ R }( WRONG % B )`

The only answer choice that leaves no remainder after the division is `\blue{A}`. `\quadFACTOR \times \pink{B} = \blue{A}`.

We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of `B` are contained within the prime factors of `A`.

`A = FACTORIZATION_A.join( "\\times" )\qquad\qquadB = FACTORIZATION_B.join( "\\times" )`

Therefore, `\blue{A}` is a multiple of `\pink{B}`.