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Here are pairs of numbers whose prime factorizations use the same prime factors:
4 = 22
32 = 25
6 = 2 x 3
24 = 23 x 3
5 = 5
625 = 54
21 = 3 x 7
63 = 32 x 7
30 = 2 x 3 x 5
180 = 22 x 32 x 5
All prime numbers have two factors: one and itself. (For example, the factors of 11 are 1 and 11.)
Example: 36 and 175
2 x 2 x 3 x 3 = 36
5 x 5 x 7 = 175
There are no common prime factors. The GCF is 1. By definition, that makes them relatively prime.
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What does a factorization look like?
The prime factorization of a number uses only primes. Ex: The prime factorization of 12 is not 6 x 2, and not 4 x 3, because 6 and 4 are not prime numbers. The prime factorization is 2 x 2 x 3. Their product is 12 and all factors are prime numbers. To get a prime factorization you are usually taught to factor through division by small prime numbers, sometimes you must use the same number more than once as in the example of 12 above 2 was used twice. Ex: find the prime factorization of 18. The smallest prime is 2... divide by 2 18 / 2 = 9 .... for the next step divide 9 by a prime 9 / 3 = 3 ... this is a prme ... it is also a factor so the prime factorization is 18 = 2x3x3 Ex. find the prime factorization of 35. 35 cannot be divided by 2, or 3, so use 5 first 35 / 5 = 7 .... since 7 is a prime we are finished. The prime factorization of 35 is 35 = 5 x 7 Some teachers teach this using a "factor tree" .. I can't type one of those on a computer.
What number is a multiple of 5 its prime factorization is a string of three numbers 2 numbers in the prime factorization are the same greater than the seventh square number?
There are a lot of possibilities. The seventh square number is 49. 5 times 5 times any other prime number will be greater than 49. 5 times any pair of prime numbers seven or greater will also satisfy the conditions.
What is the prime factorization of 95?
19*5 this answer is also the same in exponent form.The prime factorization of 95 is 5*19.5 x 19 = 95
Is the prime factorization of 20 the same thing as all the factors of 20 why or why not?
It's not, because all the factors of 20 aren't prime.
Do large numbers have more prime factors than smaller numbers?
Usually, but not necessarily and not if they're prime. All prime numbers have the same number of factors.
If you factor with different numbers do you get the same prime factorization?
Yes.
Can two numbers have the same prime factorization?
No, multiplying a set of numbers can only come out as one product. Therefore, two numbers having the same prime factorization is impossible.
Can 2 numbers have the same prime factorization?
Only if they're the same number. Every composite number has a unique prime factorization.
Is the product of a prime number the same as the prime factorization?
A prime factorization is the same as expressing a composite number as the product of its prime factors. Prime numbers don't have factorizations; they're already prime.
Is the prime factorization the same as the factor string?
Factor strings don't necessarily have to be composed entirely of prime numbers. But the longest factor string, the one that is entirely prime numbers, that's the prime factorization.
Do larger numbers have more prime factorization numbers than smaller numbers?
Usually, but not necessarily and not if they're prime. All prime numbers have the same number of factors.
Can two different numbers have the same factorization?
No.
Which numbers have a prime factorization with factors that are all the same number?
Powers of primes
How do you get the prime factorization of large numbers?
The same way as with smaller numbers, it may take longer. Just keep dividing by prime numbers until all the factors are prime.
Could 2x4x5x9x11 be the prime factorization of a number?
No because all the numbers in a prime factorization must be prime. The number 9 is not prime. It should be 3 *3. same thing with 4, should be 2*2. So what would be a prime factorization is 2x2x2x3x3x5x11.
How do you find the prime factorization of large numbers?
The same way as with smaller numbers, it may take longer. Just keep dividing by prime numbers until all the factors are prime.
Which of the numbers do not have a prime factorization that is made of all the same numbers 16 24 27 25?
24 doesn't.
