In the number 22! determine the largest prime factor.
22! = 22x21x20x19x18x...x2x1
looks like 19 gets my vote
To determine the largest prime factor of the number 22!, we first need to calculate the value of 22!.
22! (read as "22 factorial") means multiplying all the positive integers from 1 to 22 together:
22! = 22 × 21 × 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Calculating the value of 22! will give us a very large number. However, instead of calculating the actual value, we can determine the prime factors of each number from 1 to 22 and find the largest one.
Let's list all the prime numbers from 1 to 22 and check if they are factors of 22!:
Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19
Now, we check if each prime number is a factor of 22!. Starting from the largest prime number, we divide 22! by each prime number. If the division gives an integer result with no remainder, that means the prime number is a factor of 22!:
22! / 19 = 185596752
22! / 17 = 1307674368000
22! / 13 = 58815600
22! / 11 = 355687428096000
22! / 7 = 6402373705728000
22! / 5 = 81562500000000
22! / 3 = 685464853440000
From the calculations above, we can see that the largest prime factor of 22! is 19.