Divisibility Rules

Flashcards reviewing basic divisibility rules for numbers 2, 3, 4, 5, 6, and 9.

Divisibility Rule for $2$

A number is divisible by $2$ if it ends in $0$, $2$, $4$, $6$, or $8$.

Divisibility Rule for $5$

A number is divisible by $5$ if it ends in $0$ or $5$.

Divisibility Rule for $4$

A number is divisible by $4$ if its last $2$ digits are divisible by $4$.

Divisibility Rule for $3$

A number is divisible by $3$ if the sum of all its digits is divisible by $3$.

Divisibility Rule for $9$

A number is divisible by $9$ if the sum of all its digits is divisible by $9$.

Divisibility Rule for $6$

A number is divisible by $6$ if it satisfies the divisibility rules for both $2$ and $3$ at the same time.

Prime number

A natural number greater than $1$ that has exactly two distinct positive divisors: $1$ and itself.

Prime numbers between $1$ and $10$

$2$, $3$, $5$, $7$ (Total: $4$)

Prime numbers between $11$ and $20$

$11$, $13$, $17$, $19$ (Total: $4$)

Prime numbers between $21$ and $30$

$23$, $29$ (Total: $2$)

Prime numbers between $31$ and $40$

$31$, $37$ (Total: $2$)

Prime numbers between $41$ and $50$

$41$, $43$, $47$ (Total: $3$)

Prime numbers between $51$ and $60$

$53$, $59$ (Total: $2$)

All Prime numbers from $1$ to $60$

$2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$ (Total: $17$ prime numbers)

Rule for testing if a number $n$ is prime

Test divisibility by prime numbers up to $\sqrt{n}$. If no prime number less than or equal to $\sqrt{n}$ divides $n$, then $n$ is prime.

Prime numbers between $1$ and $10$

$2$, $3$, $5$, $7$ (Total: $4$)

Prime numbers between $11$ and $20$

$11$, $13$, $17$, $19$ (Total: $4$)

Prime numbers between $21$ and $30$

$23$, $29$ (Total: $2$)

Prime numbers between $31$ and $40$

$31$, $37$ (Total: $2$)

Prime numbers between $41$ and $50$

$41$, $43$, $47$ (Total: $3$)

Prime numbers between $51$ and $60$

$53$, $59$ (Total: $2$)

All Prime numbers from $1$ to $60$

$2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$ (Total: $17$ prime numbers)

Rule for testing if a number $n$ is prime

Test divisibility by prime numbers up to $\sqrt{n}$. If no prime number less than or equal to $\sqrt{n}$ divides $n$, then $n$ is prime.

Algebraic form of prime numbers greater than $3$

All prime numbers greater than $3$ can be expressed in the form $6k + 1$ or $6k - 1$, where $k$ is a positive integer.

Divisibilidad entre $2$

Un número es divisible entre $2$ si termina en $0$, $2$, $4$, $6$ u $8$.

Divisibility Rule for $2$

A number is divisible by $2$ if it ends in $0$, $2$, $4$, $6$, or $8$.

Divisibility Rule for $5$

A number is divisible by $5$ if it ends in $0$ or $5$.

Divisibility Rule for $4$

A number is divisible by $4$ if its last $2$ digits are divisible by $4$.

Divisibility Rule for $3$

A number is divisible by $3$ if the sum of all its digits is divisible by $3$.

Divisibility Rule for $9$

A number is divisible by $9$ if the sum of all its digits is divisible by $9$.

Divisibility Rule for $6$

A number is divisible by $6$ if it satisfies the divisibility rules for both $2$ and $3$ at the same time.

Prime number

A natural number greater than $1$ that has exactly two distinct positive divisors: $1$ and itself.

Prime numbers between $1$ and $10$

$2$, $3$, $5$, $7$ (Total: $4$)

Prime numbers between $11$ and $20$

$11$, $13$, $17$, $19$ (Total: $4$)

Prime numbers between $21$ and $30$

$23$, $29$ (Total: $2$)

Prime numbers between $31$ and $40$

$31$, $37$ (Total: $2$)

Prime numbers between $41$ and $50$

$41$, $43$, $47$ (Total: $3$)

Prime numbers between $51$ and $60$

$53$, $59$ (Total: $2$)

All Prime numbers from $1$ to $60$

$2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$ (Total: $17$ prime numbers)

Rule for testing if a number $n$ is prime

Test divisibility by prime numbers up to $\sqrt{n}$. If no prime number less than or equal to $\sqrt{n}$ divides $n$, then $n$ is prime.

Algebraic form of prime numbers greater than $3$

All prime numbers greater than $3$ can be expressed in the form $6k + 1$ or $6k - 1$, where $k$ is a positive integer.

Divisibilidad entre $2$

Un número es divisible entre $2$ si termina en $0$, $2$, $4$, $6$ u $8$.

Divisibilidad entre $5$

Un número es divisible entre $5$ si termina en $0$ o $5$.

Divisibilidad entre $4$

Un número es divisible entre $4$ si sus últimos $2$ dígitos son divisibles entre $4$.

Divisibilidad entre $3$

Un número es divisible entre $3$ si la suma de todos sus dígitos es divisible entre $3$.

Divisibilidad entre $9$

Un número es divisible entre $9$ si la suma de todos sus dígitos es divisible entre $9$.

Divisibilidad entre $6$

Un número es divisible entre $6$ si cumple las reglas de divisibilidad entre $2$ y $3$ al mismo tiempo.

$$1^2$$

$$1$$

$$2^2$$

$$4$$

$$3^2$$

$$9$$

$$4^2$$

$$16$$

$$5^2$$

$$25$$

$$6^2$$

$$36$$

$$7^2$$

$$49$$

$$8^2$$

$$64$$

$$9^2$$

$$81$$

$$10^2$$

$$100$$

$$11^2$$

$$121$$

$$12^2$$

$$144$$

$$13^2$$

$$169$$

$$14^2$$

$$196$$

$$15^2$$

$$225$$