Question

Помогите пожалуйста.Докажите что число 11*21*31*41*51-1111 является составным.

Answer 1

11 делится на 1 и 11 
21 делится на 1 и 21
31 делится на 1 и 31
41 делится на 1 и 41
51 делится на 1 и 51
1111 делится на 1 11 1111
Составное число должно иметь более двух делителей!

Answer 2

To prove that the number 11*21*31*41*51 - 1111 is composite, we need to show that it is divisible by a number other than 1 and itself. Let's calculate the value of this expression and check its divisibility.

Calculation:

To find the value of 11*21*31*41*51 - 1111, we can perform the multiplication and subtraction:

11*21*31*41*51 - 1111 = 1,042,731,111 - 1111 = 1,042,730,000

Divisibility Test:

To determine if this number is composite, we need to check if it is divisible by any number other than 1 and itself. One way to do this is to check for divisibility by prime numbers.

Let's check if it is divisible by some prime numbers:

1. Divisibility by 2: The number ends in 0, so it is divisible by 2. 2. Divisibility by 3: The sum of the digits (1+0+4+2+7+3+0+0+0+0) is 17, which is not divisible by 3. 3. Divisibility by 5: The number ends in 0, so it is divisible by 5. 4. Divisibility by 7: We can use the divisibility rule for 7, which states that if we subtract twice the units digit from the remaining number, the result should be divisible by 7. In this case, 1,042,730,000 - 2*0 = 1,042,730,000, which is divisible by 7. 5. Divisibility by 11: We can use the alternating sum of digits rule for 11, which states that if the alternating sum of the digits is divisible by 11, then the number is divisible by 11. In this case, (1-0+4-2+7-3+0-0+0-0) = 7, which is divisible by 11. 6. Divisibility by 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and 53: We can check these prime numbers individually, but it is not necessary as we have already found two divisors (2 and 5) other than 1 and itself.

Since we have found divisors other than 1 and itself, we can conclude that the number 11*21*31*41*51 - 1111 is composite.

Please let me know if there is anything else I can help you with!