# Book 1: Chapter 1

## 13 terms · GMAT Manhattan Book 1: Number Strategies Chapter 1: Divisibility and Primes

### An integer is divisible by 2

If the integer is even

### An integer is divisible by 3

If the sum of the integer's DIGITS is divisible by 3

### An integer is divisible by 4

If the integer is divisible by 2 twice

### An integer is divisible by 5

If the integer ends in 0 or 5

### An integer is divisible by 6

If the integer is divisible by both 2 and 3

### An integer is divisible by 8

If the integer is divisible by 2 three times, of if the last three digits are divisible by 8

### An integer is divisible by 9

If the sum of the integer's digits is divisible by 9

### An integer is divisible by 10

If the integer ends in 10

### An integer is always a _________ and __________ of itself.

factor and multiple

### Mnemonic for factors and multiples

Fewer Factors and More Multiples

### Other ways to say: 3 is a factor of 12; 12 is divisible by 3; or 12 is a multiple of 3

12/3 is an integer; 12/3 yields a remainder of 0; 12 = 3n, where n is an integer; 12 items can be shared among 3 ppl so that wach person has the same number of items

### Addition and Subtraction of multiples

If you add or subtract multiples of N, the result is a multiple of N

### Factor Foundation Rule

If a is a factor of b, and b is a factor of c, then a is a factor of . AKA any integer is divisible by all of its factors and also by the FACTORS of its factors

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