GMAT-Divisibility Definitions

Question 1

Divisible

Answer 1

Definition:
Divides evenly into.
Divides so that the remainder is zero.

Notes:
The number 6 is divisible by 1, 2, 3,
and 6.

Question 2

Multiple

Answer 2

Definition:
Multiples of x are found by multiplying
x by any integer.

Notes:
The multiples of 6 are 6, 12, 18, 24, etc.

Question 3

Factor/Divisor

Answer 3

Definition:
Factors of x are integers that multiply by
other integers to yield x.

Notes:
Usually it’s most worthwhile to think of
factors in pairs. The factors of 12 are (1
and 12), (2 and 6), and (3 and 4).

Question 4

Least Common

Multiple

Answer 4

Definition:
The smallest possible integer that is
divisible by all of the integers
mentioned.

Notes:
12 is the least common multiple of 6
and 4. 24 is also the least common
multiple of 3 and 8.

Question 5

Greatest Common

Factor

Answer 5

Definition:
The greatest integer that is a factor of all
of the integers mentioned.

Notes:
12 is the greatest common factor of 12
and 24. 8 is the greatest common factor
of 16 and 24.

Question 6

Even

Answer 6

Definition:
Any integer that is divisible by two.

Notes:
Zero is even.

Question 7

Odd

Answer 7

Definition:
Any integer that is not divisible by two.

Notes:
Fractions/decimals are neither even nor
odd.

Question 8

Prime

Answer 8

Definition:
A number with exactly two distinct
factors (those factors being 1 and the
number itself).

Notes:
Negative numbers are not prime.
1 is not prime. 2 is the smallest prime
and the only even prime.

Question 9

If a number is divisible by x …

Answer 9

then that number is divisible by all factors of x.

Example:
If 100/ 10 then 100/ 2 and 100/5

Question 10

If a number is a multiple of x …

Answer 10

then that number is NOT necessarily a multiple of the other multiples
of x.

Example:
multiple of 3s is 3, 6, 9, 12, 15
number is 9 is not a multiple of 15

Question 11

If a number is a multiple of x and y …

Answer 11

then that number will be a multiple of the least common multiple of x and y.

Example:
x=3 and y=6
multiple of 3s is 3, 6, 9, 12
multiple of 6s is 6, 12, 18
number is 12 and is LCM of 3 and 6

Question 12

The least common multiple of x and y is …

Answer 12

not necessarily the same as the product of x and y.

Example:
x=3 and y=6
multiple of 3s is 3, 6, 9, 12
multiple of 6s is 6, 12, 18
number is 12 and is LCM of 3 and 6 

product of x and y is 3*6= 18