Composite number 1,390,329 prime factorization (decomposing, breaking down into prime factors), written as a product of primes (with exponents, powers)

The prime factorization of the composite number 1,390,329

The natural numbers that are only divisible by 1 and themselves are called prime numbers.

A composite number is a natural number that has at least one other factor than 1 and itself.

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


1,390,329 is not a prime number but a composite one.
1,390,329 can be written as a product of prime numbers:

The prime factorization of the composite number 1,390,329:
1,390,329 = 3 × 3 × 241 × 641

The prime factorization, written as a product of prime factors, with exponents (powers): *
1,390,329 = 32 × 241 × 641

* A number written with exponents is a base raised to the exponent (we say: the base raised to the power of the exponent). The exponent indicates how many times the base is multiplied by itself: 53 = 5 × 5 × 5 = 125. We say 5 raised to the power of 3. 53 is the power, 5 is the base, 3 is the exponent and 125 is the value of the power.

The prime numbers are the building blocks of all the numbers except for 0 and 1.

The composite numbers consist of prime numbers that are multiplied together.

There is only one prime number that is an even number: 2. All the other prime numbers are odd numbers.

The prime factorization of a number, how is it done

Let's learn by having an example:
Take number 220 and build its prime factorization

We need the list of the first prime numbers, ordered from 2 up to, let's say, 20:
2, 3, 5, 7, 11, 13, 17, 19.
The prime numbers are the building blocks of the composite numbers.


1. Start by dividing 220 by the smallest prime number, 2:
220 ÷ 2 = 110; remainder = 0 =>
220 is divisible by 2 => 2 is a prime factor of 220:
220 = 2 × 110.


2. Divide the result of the previous operation, 110, by 2, again:
110 ÷ 2 = 55; remainder = 0 =>
110 is divisible by 2 => 2 is a prime factor of 110:
220 = 2 × 110 = 2 × 2 × 55.


3. Divide the result of the previous operation, 55, by 2, again:
55 ÷ 2 = 27 + 1; remainder = 1 =>
55 is not divisible by 2.


4. Move on to the next prime number, 3. Divide 55 by 3:
55 ÷ 3 = 18 + 1; remainder = 1 =>
55 is not divisible by 3.


5. Move on to the next prime number, 5. Divide 55 by 5:
55 ÷ 5 = 11; remainder = 0 =>
55 is divisible by 5 => 5 is a prime factor of 55:
220 = 2 × 2 × 55 = 2 × 2 × 5 × 11.


6. Notice that the remaining factor, 11, is a prime number, so we've already found all the prime factors of 220.


Conclusion, the prime factorization of 220:
220 = 2 × 2 × 5 × 11.
This can be written in a condensed form, in exponential notation:
220 = 22 × 5 × 11.

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The prime factorization of a number N = Dividing the number N into smaller numbers that are prime. By multiplying these smaller prime numbers one gets the number N.

A prime number is a natural number that is only divisible by 1 and itself. 1 is not considered a prime number.

Prime numbers. Composite numbers. The prime factorization of composite numbers (decomposing, breaking down numbers into prime factors)


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