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What number has the prime factorization of 2 to the exponent of 2 x 3 x 5 to the exponent of 2 x 7?
32
Which number has exactly 15 factors?
The number that has exactly 15 factors is 28. To determine the number of factors a number has, you can prime factorize the number and then add 1 to each exponent in the prime factorization and multiply these numbers together. In the case of 28, the prime factorization is 2^2 * 7^1, so the number of factors is (2+1) * (1+1) = 3 * 2 = 6. To have exactly 15 factors, the number needs to be a square of a prime number, so 28 = 2^2 * 7^1 fits this criteria.
What is a number written as the product of its prime factors?
The prime factorization of a number is writing it as a product of its prime factors.
How is prime factorization different from finding factors of a number?
All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.
The n in x'' indicatiing the number of factors of x?
exponent
Will prime factorization help find the number of factors of any number?
Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors.
Can you predict the number of factors of any number by writing the prime factorization using exponents then adding one to the exponent and then finding the products of these numbers?
Yes.
What is a number written as the product of prime factors?
a prime factorization
How do you calculate the number of factors of a number?
List the prime factorization of the number by exponents. Remember that if a number does not have an exponent, the exponent "1" is implied. Add one to each exponent and multiply. That is the total number of factors. 2^3 x 3^2 = 72 4 x 3 = 12 72 has twelve factors. If there is only one prime factor, add one and there you are. 2^4 = 16 16 has five factors.
Can you tell when you have all of the factors for a number before you have built every possible array explain?
If you know the prime factorization of a number, you can tell how many factors it has. Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors. 10 = 2 x 5 = 21 x 51 2 x 2 = 4 10 has four factors.
A number written as the pruduct of its prime factors is called what?
a prime factorization
What is a number written as a product of its prime factors?
That's a prime factorization.
What is it called when a number is written as the product of its prime factors?
prime factorization
What is a number written as the product of all its prime factors?
That's a prime factorization.
A number written as the product of all its prime factors is called?
A prime factorization
How many in factors in 156?
You can find out the number of factors of any number from its prime factorization by adding one to each exponent and multiplying. The prime factorization of 156 is 2^2 x 3^1 x 13^1 3 x 2 x 2 = 12 156 has 12 factors.
How do you determine the number of divisors using the prime factorization and its exponents?
Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors. 10 = 2 x 5 = 21 x 51 2 x 2 = 4 10 has four factors. 72 = 23 x 32 4 x 3 = 12 72 has twelve factors. Square numbers can be tricky. The prime factorization of 9 should be written as 32, not 3 x 3. Adding 1 to the 2 gives you 3. 9 has three factors.
