Finding the highest power of 7 in 100!

When we are asked to find the highest power of a prime number in a factorial, we need to follow a specific method. Here is how we can find the highest power of 7 in 100!:

Step 1: Find the quotient of 100 divided by 7. We get 14.285714...

Step 2: Round down this quotient to the nearest whole number. We get 14.

Step 3: Find the quotient of 100 divided by 49 (which is 7 squared). We get 2.0408...

Step 4: Round down this quotient to the nearest whole number. We get 2.

Step 5: Find the quotient of 100 divided by 343 (which is 7 cubed). We get 0.2915...

Step 6: Round down this quotient to the nearest whole number. We get 0.

Step 7: Add the results from Step 2 and Step 4. We get 16.

Therefore, the highest power of 7 in 100! is 7^16.

Important Formulas: Number System

Here are some important formulas related to Number System that can be helpful in solving problems:

1. Prime Numbers: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.

2. Composite Numbers: A composite number is a positive integer that has at least one positive divisor other than 1 and itself. Examples of composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc.

3. Even Numbers: An even number is an integer that is divisible by 2. Examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.

4. Odd Numbers: An odd number is an integer that is not divisible by 2. Examples of odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, etc.

5. HCF (Highest Common Factor): HCF of two or more numbers is the greatest number that divides each of them without leaving a remainder. For example, the HCF of 12 and 18 is 6.

6. LCM (Least Common Multiple): LCM of two or more numbers is the smallest number that is a multiple of each of them. For example, the LCM of 3 and 4 is 12.

7. Divisibility Rules: There are certain rules that can be used to determine whether a number is divisible by another number. For example, a number is divisible by 2 if its last digit is even, and it is divisible by 3 if the sum of its digits is divisible by 3.

8. Base Conversion: In base 10

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