IS 720 is a composite number?

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Composite number 720 prime factorization (decomposing, breaking down into prime factors), written as a product of primes (with exponents, powers)

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.

720 is not a prime number but a composite one. 720 can be written as a product of prime numbers.

The prime factorization of the composite number 720: 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5

The prime factorization, written in a condensed way, as a product of prime factors, with exponents (powers): *720 = 24 × 32 × 5

* 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 numbers up to 1,000

The prime numbers up to 10,000

The prime factorization of a number, how is it done

Let's learn by having an example: - Take the 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.

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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.

Prime or composite numbers? The last 5 numbers on which the prime factorization has been performed

Check whether a number is prime or not. Run the prime factorization of the composite numbers

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)

• The Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
• The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers, in a way that is unique, except for the order of the prime factors.
• The number 1 is not considered prime, so the first prime number is 2.
• If the number 1 were considered a prime number, then the prime factorization of the number 15 could be written as: 15 = 3 × 5 OR 15 = 1 × 3 × 5 - these two representations would be considered different prime factorizations of the same number, so the theorem above would have no longer been valid.

• The natural numbers that are evenly dividing only by 1 and themselves are called prime numbers.
• Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and so on.
• If a number is prime, it cannot be factored down to other prime factors, it is divisible only by 1 and itself - the number itself is called in this case an IMPROPER FACTOR (or an improper divisor). Some people also consider 1 as an improper factor.

• A composite number is a natural number that has at least one factor (divisor) other than 1 and the number itself.
• A composite number is also any natural number larger than 1 that is not a prime number.
• Examples of composite numbers: 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26 and so on.

• A prime number can't be factored down to other prime factors, but a number that is a composite can, as shown below:
• Example 1: 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime, it's a composite number. 6 can be written as a product of factors in different ways, as: 6 = 1 × 6, or 6 = 1 × 2 × 3 or 6 = 2 × 3. But its prime factorization, regardless the order of the factors, is always: 6 = 2 × 3.
• Example 2: 120 can be written as a product of factors in different ways, as 120 = 4 × 30 or 120 = 2 × 2 × 2 × 15 or 120 = 2 × 2 × 2 × 3 × 5. Its prime factorization is always: 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5 - the last form of writing is the condensed form, with exponents, of the first form, the longer one.
• * Note: 23 = 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. In this example, 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 23 is the power and 8 is the value of the power.

• Why is it important to know about the prime factorization of the numbers?
• The prime factorization is useful when calculating the greatest common factor, GCF, of numbers (also called the greatest common divizor GCD, or the highest common factor, HCF).
• GCF is needed when reducing (simplifying) fractions to the lowest terms.
• The prime factorization comes in handy when calculating the least common multiple, LCM, of numbers - this is needed when adding or subtracting ordinary fractions, for example...
• And the examples could continue (numbers divisibility, calculating all the factors of a number starting from its prime factorization, and so on...).

• More examples of prime numbers:
• 181 is divisible only by 181 and 1, so 181 is a prime number.
• 2,341 is divisible only by 2,341 and 1, so 2,341 is a prime number.
• 6,991 is divisible only by 6,991 and 1, so 6,991 is a prime number.
• This is the list of all the prime numbers, from 1 up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
• The prime numbers are used as basic blocks when building the prime factorization of the composite numbers. So we could say that the prime numbers really are the basic blocks of the composite numbers.

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples

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