Question

Используя признаки делимости чисел2,3,5и9 докажите,что числа:

Answer 1

1. 117=1+1+7=9, следовательно, 117 делится на 9 и 3. 122 делится на 2, т.к. последняя цифра четная. 205 делится на 5, т.к. последняя цифра 0 или 5, 219 делится на 3, т.к. сумма чисел (2+1+9) делится на 3. 393 так-же на 3 делится, 422 на 2 т.к. последнее число четное, 535 делится на 5 т.к. последня пятерка, 927 делится на 9 и 3, т.к. сумма чисел делится на 9

2. все эти числа можно разделить только на единицу и на себя само, следовательно эти числа являются простыми.

Answer 2

Using Divisibility Rules to Prove Properties of Numbers

To prove properties of numbers using the divisibility rules of 2, 3, 5, and 9, we can apply these rules to the given numbers and analyze their divisibility characteristics.

Number 1: 30 - Divisibility by 2: A number is divisible by 2 if its last digit is even. In the case of 30, the last digit is 0, which is even, so 30 is divisible by 2. - Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 30, the sum of its digits is 3 + 0 = 3, which is divisible by 3, so 30 is divisible by 3. - Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. In the case of 30, the last digit is 0, so 30 is divisible by 5. - Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. For 30, the sum of its digits is 3 + 0 = 3, which is not divisible by 9, so 30 is not divisible by 9.

Therefore, based on the divisibility rules: - 30 is divisible by 2, 3, and 5. - 30 is not divisible by 9.

Number 2: 45 - Divisibility by 2: A number is divisible by 2 if its last digit is even. In the case of 45, the last digit is 5, which is not even, so 45 is not divisible by 2. - Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 45, the sum of its digits is 4 + 5 = 9, which is divisible by 3, so 45 is divisible by 3. - Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. In the case of 45, the last digit is 5, so 45 is divisible by 5. - Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. For 45, the sum of its digits is 4 + 5 = 9, which is not divisible by 9, so 45 is not divisible by 9.

Therefore, based on the divisibility rules: - 45 is divisible by 3 and 5. - 45 is not divisible by 2 and 9.

In conclusion, the properties of the numbers 30 and 45, based on the given divisibility rules, are as follows: - 30 is divisible by 2, 3, and 5, but not by 9. - 45 is divisible by 3 and 5, but not by 2 and 9.