# What is the number of distinct primes dividing 12! + 13! +14! ?

To find the number of distinct prime numbers dividing (12! + 13! + 14!), we first need to factorize the expression.

[12! + 13! + 14! = 12! \left(1 + 13 + 13 \times 14\right) = 12! \times 182]

Now, we need to factorize (12!) to find its prime factors. The prime factorization of (12!) is:

[12! = 2^{10} \times 3^5 \times 5^2 \times 7 \times 11]

Next, we need to find the prime factorization of 182:

[182 = 2 \times 91 = 2 \times 7 \times 13]

Now, we can combine the prime factorizations of (12!) and 182 to find the prime factorization of (12! \times 182):

[12! \times 182 = 2^{10} \times 3^5 \times 5^2 \times 7^2 \times 11 \times 13]

Thus, the distinct prime factors of (12! + 13! + 14!) are (2), (3), (5), (7), (11), and (13). Therefore, the number of distinct prime numbers dividing (12! + 13! + 14!) is 6.

By signing up, you agree to our Terms of Service and Privacy Policy

are

By signing up, you agree to our Terms of Service and Privacy Policy

Five distinct primes divide

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you simplify #-11 5/8 - (-4 3/7)#?
- How do you find the two solutions to the #sqrt(145)#?
- What is three fourths of a number is 192?
- What is the new temperature in Chicago, if one morning it was #-8^\circ F# and over the next six hours the temperature rose 25 degrees Fahrenheit?
- How do you simplify #21-8(v-3)+3+7v#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7