Question

Find the highest power of 24 in 100!

Answer 1

Answer:

100 complete the answer

Answer 2

Answer:

32

Step-by-step explanation:

Step 1

Prime factorize the given number to find the prime factor and its highest power.

Now, prime factorization of 24 = 2³ * 3

Step 2

The highest power of 2³ in 100! = [(Maximum power of 2 in 100!) / 3]

                   = [ ( 100/2¹ + 100/2² + 100/2³ + 100/2⁴ + 100/2⁵ + 100/2⁶) / 3]

                    = [(50 + 25+ 12 + 6 + 3 + 1 ) / 3]

                    = 97 / 3

                    =32

And, the highest power of 3 in 100! =  [(Maximum power of 3 in 100!) / 1 ]

                                      = [ ( 100/3¹ + 100/3² + 100/3³ + 100/3⁴ ) / 1]

                                      = 33 + 11 + 3 + 1

                                      = 48

Since the maximum power of 2³ is less than the maximum power of 3 the maximum power of 24 in 100! will be equal to the maximum power of 2³ in 100! which is 32.