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.
47 is a prime number.
41 is a prime number.
11 is a prime number.
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.
19 is a prime number so the factorization is 1 x 19
19 is a prime number in its own right and needs no exponents
11 is a prime number in its own right and needs no exponents
11 is already prime. No factorization or exponents needed.
2^5
47 is a prime number.
41 is a prime number.
11 is a prime 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.
19 is a prime number so the factorization is 1 x 19
None. 887 is a prime number.
2^3*3
3^2 x 5