Divisibility And Factoring

Question 1

How to exhaustively find all factors

Answer 1

Make a factor table. Start with smallest number in left column and pair it therefore with the largest. So 1 and the number itself… progress to the next smallest number. Your second small number will be a factor of the first large number. Pattern continues

Question 2

What are the smallest primes less than 20?

Answer 2

2, 3, 5, 7, 11, 13, 17 & 19

Question 3

Factor trees are useful…

Answer 3

To explore the relations of all pairs and discover all prime factors which are the building blocks. You can even discover the value of a variable by breaking it all the way down to its PF and then finding the product

Question 4

When 2 factors are given about the same variable… or it states that a variable is divisible by 2 numbers

Answer 4

You will form 2 respective factors trees. You will discover their PFs. You may combine the PFs revealed from the factor trees IF they do not share a common PF.
X is divisible by 28 (2, 2, & 7) and by 15 (3 & 5). None of the PFs overlap. Therefore, X’s greatest/largest factor is the product of (2, 2, 7, 3, & 5).

Question 5

If a number is divisible by X & Y, it’ll be divisible by…

Answer 5

The LCM of X & Y (aka the greatest number that they can be divided by) Strip out unnecessary factors when you observe overlap

Question 6

Possibility for zero in denominator…

Answer 6

Can be ignored. GMAT never tests undefined math… factor the numerator to get your answer

Question 7

Want to solve for a variable but it’s on the bottom?

Answer 7

just take reciprocal of both sides