Question

Find the remainder when 1!+2!+3!+...+15! is divided by 15

Answer 1

Answer:

• 3

Step-by-step explanation:

We know that

• n! = 1*2*3*...*n

We also know that

• 15 = 3*5

Since 5! = 1*2*3*4*5 is divisible by 15:

• any n! with n ≥ 5 is divisible by 15.

We need to find the remainder when 1! + 2! + 3! + 4! is divided by 15 as all the rest are divisible by 15.

The sum is:

• 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

The remainder is:

• 33/15 = 2 rem 3

As we see the remainder is 3

Answer 2

Question :-

Find the remainder when 1!+2!+3!+...+15! is divided by 15

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Solution :-

Given Information :-

• 1!+2!+3!+...+15! is divided by 15

To Find :-

• The Remainder

Calculation :-

• Concept :-

We already know that,

n! = 1 × 2 × 3 × ... × n

$\big \&$

15 = 3 × 5

∵ 5! = 1 × 2 × 3 × 4 × 5 is divisible by 15

⇒ n! { n ≥ 5 } can be divided by 15.

Now, according to our question,

⇒ 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

⇒ Remainder = $\sf \frac{33}{15}$

⇒ 2 rem 3

⇒ Remainder = 3

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Final Answer :-

The Remainder is 3

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