All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
Prime numbers are used to find the product of the prime factors of composite numbers.
Both of these will work:48 = 2 x 2 x 2 x 2 x 348 = 24 x 3
3*5*11
23 x 33 = 216
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.
The fundamental theorem of arithmetic says any integer can be factored into a unique product of primes. The is the prime factored form.
As a product of its prime factors: 2*3*7 = 42
Prime numbers are used to find the product of the prime factors of composite numbers.
Both of these will work:48 = 2 x 2 x 2 x 2 x 348 = 24 x 3
As a product of its prime factors: 5^3 times 13 = 1625
To express 63 as a product of prime factors in index form, we first need to find the prime factors of 63. 63 can be factored as 3 x 3 x 7. This can be written in index form as 3^2 x 7. Therefore, 63 as a product of prime factors in index form is 3^2 x 7.
3*5*11
23 x 33 = 216
2 x 3 x 5
289 = 17 x 17
It is 23 and 1 because 23 is a prime number
2*3*3*5 = 90