243 is a multiple of 3 and 3 is the only prime number that is a factor of 243, that's
to say 3 is the unique prime factor of 243. Since 243 is not a prime number, 243 has more than two factors.
243 is a composite number with 6 factors, here are the 6 factors of 243:
**1; 3; 9; 27; 81; 243.**

A factor of 243 is a whole number that we can multiply by another whole number to retrieve 243.

Example: 27 is a multiple of 243 because we can retrieve 243 by multiplying 27 with another positive integer that is equal to 9. 27*9=243. Since 27 multiplied by 9 gives 243 then 27 and 9 are both factors of 243.

Remark: If we divide 243 by one of its factors we get as quotient another factor of 243.

Example: 81 is a factor of 243, so 243 divided by 81 gives as quotient 3 that is another factor of 243 and the remainder of the division is equal to zero.

Here are all the multiplications of two integers that the product is equal to 243:**1*243=243; 3*81=243; 9*27=243.**

**The prime factorization of 243 is: 3^5.**

243 is not a multiple of 2 then 243 is an odd number.

**Factors of 243:**

Justify why 1; 3; 9; 27; 81 and 243 are factors of 243?

Note: A factor of 243 is a whole number that can divide 243 by giving an integer quotient and a remainder that is equal to zero or it's a whole number that we can multiply with another whole number to get 243 as product.

1 is a factor of 243 because 243 divided by 1 is equal to 243 and the remainder of the division is equal to zero.

3 is a factor of 243 because 243 divided by 3 gives 81 as quotient and the remainder of the division is equal to zero.

9 is a factor of 243 because 243 divided by 9 gives 27 as quotient and the remainder of the division is equal to zero.

27 is a factor of 243 because the multiplication of 27 and 9 gives 243 as product.

81 is a factor of 243 because the multiplication of 81 by 3 gives 243 as product.

243 is a factor of 243 because the multiplication of 243 by 1 gives 243 as product.

**Multiples of 243:**

Justify if the following natural numbers are multiples of 243: 234; 500; 1215; 486; 729; 2430; 1701; 3159; 3162; 5346; 5103; 5113; 7290; 1944; 1948; 3645; 4131; 2673; 3402; 3408; 8019.

Note: A positive integer is a multiple of 243 if its division by 243 gives a whole number as quotient and a remainder that is equal to zero.

If a natural number is a multiple of 243 then 243 is its factor.

243 is an odd number so 243 can have even numbers or odd numbers as multiples.

If we divide 243 by 243 we get an integer quotient that is equal to 1 and the remainder of the division is equal to zero so 243 is a multiple of 243 (243 and 1 are factors of 243).

500 is not a multiple of 243 because 500 divided by 243 gives 2 as quotient and the remainder of the division is different from zero so 243 is not a factor of 500.

By dividing 1215 by 243 we get 5 as quotient and the remainder of that division is equal to zero so 1215 is a multiple of 243 and 5 (243 and 5 are factors of 1215).

486 is divisible by 243 because 486 divided by 243 gives 2 as quotient and zero remainder so 243 is a factor or divisor of 486.

729 is the product of the multiplication of 243 by 3 so 729 is a common multiple of 243 and 3 (243 and 3 are factors of 729).

243 is a factor of 2430 because the division of 2430 by 243 gives 10 as quotient and the remainder of the division is equal to zero so 2430 is a multiple of 243.

By multiplying 243 by 7 we get 1701 as product so 1701 is a common multiple of 243 and 7 (243 and 7 are divisors or factors of 1701).

3159 is a multiple of 243 and 243 is a factor of 3159 because the quotient of the division of 3159 by 243 is equal to 13 and the remainder of that division is equal to zero.

243 is not a factor of 3162 because 3162 is not divisible by 243 so 3162 is not a multiple of 243.

5346 divided by 243 gives 22 as quotient and a remainder that is equal to zero so 5346 is a common multiple of 243 and 22 (243 and 22 are factors of 5346).

The multiplication of 243 by 21 gives 5103 as product so 5103 is a commun multiple of 243 and 21 (243 and 21 are divisors of 5103).

5113 is not a factor of 243 because the division of 5113 by 243 gives 21 as quotient and a remainder that is not equal to zero.

If we multiply 243 by 30 we get 7290 so 7290 is a commun multiple of 243 and 30 (243 and 30 are factors of 7290).

1944 divided by 243 is equal to 8 and the remainder of the division is equal to zero so 1944 is a multiple of 243 and 243 is a factor of 1944.

The division of 1948 by 243 gives 8 as quotient and a remainder that is equal to 4 so 1948 is not a multiple of 243 and 243 is not a factor of 1948.

3645 is a common multiple of 243 and 15 because the multiplication of 243 and 15 gives 3645 as product so 243 and 15 are factors of 3645.

By multiplying 243 by 17 we get 4131 as product so 4131 is a multiple of 243 and 17 (243 and 17 are factors of 4131).

By dividing 2673 by 243 we get 11 as quotient and zero remainder so 2673 is a multiple of 243 and 11 (243 and 11 are factors of 2673).

3402 is divisible by 243 because the division of 3402 by 243 gives 14 as quotient and a remainder that is equal to zero so 3402 is a common multiple of 243 and 14 (243 and 14 are factors of 3402).

3408 is not divisible by 243 because we cannot find a positive integer that we can multiply by 243 to get 3408 so 243 is not a factor of 3408 and 3408 is not a multiple of 243.

8019 divided by 243 gives 33 as quotient and the remainder of the division is equal to zero so 8019 is a multiple of 243 and 243 is a factor of 8019.

**Arithmetic and algebra expressions:**

**Positive integer:** Positive integers or natural numbers are numbers that are written only by using the combination of the ten existing
digits (0; 1; 2; 3; 4; 5; 6; 7; 8; 9). The natural numbers are infinite, we cannot list them all.

The first number that is a natural number is 0.

**Rational number: **Rational numbers are numbers we can write them as fractions that the numerators are
relative integers and the denominators are whole numbers different from zero.

** Fraction:** A fraction is a division where the dividend is called the numerator and the divisor is called the denominator.

**Factors :** A factor of a whole number is a positive integer that can divide that whole number, each whole number
has at least two factors.

**Common factors: **If a natural number divides two numbers by giving an integer quotient and zero remainder then that
natural number is a common factor or common divisor of the two numbers.

**Prime factors:** A prime factor of a whole number is its factor that is a prime number.

**Composite numbers:** a composite number is a natural number that is not a prime number.

** Even numbers: **An even number is a positive integer that is divisible by 2.

** Odd numbers:** An odd number is a positive integer that is not divisible by 2.

** Decimals :** decimals are all numbers that can be written with a point or not, all natural number are decimals but
all decimal numbers are not natural numbers.

** Substraction :** a subtraction is one of the four arithmetic operations that allows you to tell the difference between two numbers.

** Divisibility rules :** a rule of divisibility helps to know if a natural number is divisible by another
natural number or not.

**find the lcm and the gcf of two integers**

**find the first n multiples of an integer**

**find the multiples of an integer inside an interval**

**retrieve prime numbers inside an interval**

**retrieve the irreducible value of a fraction**

A factor of 243 is a whole number that we can multiply by another whole number to retrieve 243.

Example: 27 is a multiple of 243 because we can retrieve 243 by multiplying 27 with another positive integer that is equal to 9. 27*9=243. Since 27 multiplied by 9 gives 243 then 27 and 9 are both factors of 243.

Remark: If we divide 243 by one of its factors we get as quotient another factor of 243.

Example: 81 is a factor of 243, so 243 divided by 81 gives as quotient 3 that is another factor of 243 and the remainder of the division is equal to zero.

Here are all the multiplications of two integers that the product is equal to 243:

243 is not a multiple of 2 then 243 is an odd number.

Justify why 1; 3; 9; 27; 81 and 243 are factors of 243?

Note: A factor of 243 is a whole number that can divide 243 by giving an integer quotient and a remainder that is equal to zero or it's a whole number that we can multiply with another whole number to get 243 as product.

1 is a factor of 243 because 243 divided by 1 is equal to 243 and the remainder of the division is equal to zero.

3 is a factor of 243 because 243 divided by 3 gives 81 as quotient and the remainder of the division is equal to zero.

9 is a factor of 243 because 243 divided by 9 gives 27 as quotient and the remainder of the division is equal to zero.

27 is a factor of 243 because the multiplication of 27 and 9 gives 243 as product.

81 is a factor of 243 because the multiplication of 81 by 3 gives 243 as product.

243 is a factor of 243 because the multiplication of 243 by 1 gives 243 as product.

Justify if the following natural numbers are multiples of 243: 234; 500; 1215; 486; 729; 2430; 1701; 3159; 3162; 5346; 5103; 5113; 7290; 1944; 1948; 3645; 4131; 2673; 3402; 3408; 8019.

Note: A positive integer is a multiple of 243 if its division by 243 gives a whole number as quotient and a remainder that is equal to zero.

If a natural number is a multiple of 243 then 243 is its factor.

243 is an odd number so 243 can have even numbers or odd numbers as multiples.

If we divide 243 by 243 we get an integer quotient that is equal to 1 and the remainder of the division is equal to zero so 243 is a multiple of 243 (243 and 1 are factors of 243).

500 is not a multiple of 243 because 500 divided by 243 gives 2 as quotient and the remainder of the division is different from zero so 243 is not a factor of 500.

By dividing 1215 by 243 we get 5 as quotient and the remainder of that division is equal to zero so 1215 is a multiple of 243 and 5 (243 and 5 are factors of 1215).

486 is divisible by 243 because 486 divided by 243 gives 2 as quotient and zero remainder so 243 is a factor or divisor of 486.

729 is the product of the multiplication of 243 by 3 so 729 is a common multiple of 243 and 3 (243 and 3 are factors of 729).

243 is a factor of 2430 because the division of 2430 by 243 gives 10 as quotient and the remainder of the division is equal to zero so 2430 is a multiple of 243.

By multiplying 243 by 7 we get 1701 as product so 1701 is a common multiple of 243 and 7 (243 and 7 are divisors or factors of 1701).

3159 is a multiple of 243 and 243 is a factor of 3159 because the quotient of the division of 3159 by 243 is equal to 13 and the remainder of that division is equal to zero.

243 is not a factor of 3162 because 3162 is not divisible by 243 so 3162 is not a multiple of 243.

5346 divided by 243 gives 22 as quotient and a remainder that is equal to zero so 5346 is a common multiple of 243 and 22 (243 and 22 are factors of 5346).

The multiplication of 243 by 21 gives 5103 as product so 5103 is a commun multiple of 243 and 21 (243 and 21 are divisors of 5103).

5113 is not a factor of 243 because the division of 5113 by 243 gives 21 as quotient and a remainder that is not equal to zero.

If we multiply 243 by 30 we get 7290 so 7290 is a commun multiple of 243 and 30 (243 and 30 are factors of 7290).

1944 divided by 243 is equal to 8 and the remainder of the division is equal to zero so 1944 is a multiple of 243 and 243 is a factor of 1944.

The division of 1948 by 243 gives 8 as quotient and a remainder that is equal to 4 so 1948 is not a multiple of 243 and 243 is not a factor of 1948.

3645 is a common multiple of 243 and 15 because the multiplication of 243 and 15 gives 3645 as product so 243 and 15 are factors of 3645.

By multiplying 243 by 17 we get 4131 as product so 4131 is a multiple of 243 and 17 (243 and 17 are factors of 4131).

By dividing 2673 by 243 we get 11 as quotient and zero remainder so 2673 is a multiple of 243 and 11 (243 and 11 are factors of 2673).

3402 is divisible by 243 because the division of 3402 by 243 gives 14 as quotient and a remainder that is equal to zero so 3402 is a common multiple of 243 and 14 (243 and 14 are factors of 3402).

3408 is not divisible by 243 because we cannot find a positive integer that we can multiply by 243 to get 3408 so 243 is not a factor of 3408 and 3408 is not a multiple of 243.

8019 divided by 243 gives 33 as quotient and the remainder of the division is equal to zero so 8019 is a multiple of 243 and 243 is a factor of 8019.

The first number that is a natural number is 0.