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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.
What else can I help you with?
What is the prime factorization of 47 using exponents?
47 is a prime number.
What is the prime factorization of 11 using exponents?
11 is a prime number.
What is the prime factorization using exponents of 41?
41 is a prime number.
How many ways 14630 can be written as product of two numbers?
To determine how many ways 14630 can be expressed as a product of two numbers, we first need its prime factorization. The prime factorization of 14630 is (2 \times 5 \times 1463). The number of divisors can be calculated from the exponents of the prime factors; since (2^1, 5^1, \text{ and } 1463^1) each have an exponent of 1, the total number of divisors is ((1+1)(1+1)(1+1) = 2 \times 2 \times 2 = 8). Each pair of divisors ( (d, \frac{14630}{d}) ) gives a product of 14630, so the number of unique pairs is half of the total number of divisors, leading to 4 ways to express 14630 as a product of two numbers.
What is the prime factorization of 19 using exponents?
19 is a prime number so the factorization is 1 x 19
What is prime factorization of 19 using exponents?
19 is a prime number in its own right and needs no exponents
What is prime factorization of 11 using exponents?
11 is a prime number in its own right and needs no exponents
What is the prime factorization in exponential form for the number 11?
11 is already prime. No factorization or exponents needed.
what is the prime factorization of the number 32 using exponents?
2^5
What is the prime factorization of 47 using exponents?
47 is a prime number.
What is the prime factorization using exponents of 41?
41 is a prime number.
What is the prime factorization of 11 using exponents?
11 is a prime number.
How many ways 14630 can be written as product of two numbers?
To determine how many ways 14630 can be expressed as a product of two numbers, we first need its prime factorization. The prime factorization of 14630 is (2 \times 5 \times 1463). The number of divisors can be calculated from the exponents of the prime factors; since (2^1, 5^1, \text{ and } 1463^1) each have an exponent of 1, the total number of divisors is ((1+1)(1+1)(1+1) = 2 \times 2 \times 2 = 8). Each pair of divisors ( (d, \frac{14630}{d}) ) gives a product of 14630, so the number of unique pairs is half of the total number of divisors, leading to 4 ways to express 14630 as a product of two numbers.
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.
What is the prime factorization of 19 using exponents?
19 is a prime number so the factorization is 1 x 19
What is the prime factorization of 887 using exponents?
None. 887 is a prime number.
What is the prime factorization using exponents for the number 24?
2^3*3
