Question

При делении натурального числа на 45 в остатке получилось 21. Каким будет остаток от деления этого числа на 15?

Answer 1

 Надо к 45 прибавить 21 и разделить на 15 вот и получается  45+21/15=4.4

Answer 2

Division and Remainders

When a natural number is divided by 45, the remainder is 21. We want to find the remainder when the same number is divided by 15.

The relationship between the remainders of a number when divided by different divisors can be determined using the concept of modular arithmetic. In this case, we can use the fact that if a number leaves a remainder of 21 when divided by 45, it will leave the same remainder when divided by any multiple of 45.

Modular Arithmetic: - When a number is divided by a divisor, the remainder can be expressed as the difference between the number and the largest multiple of the divisor that is less than or equal to the number.

Let's calculate the remainder when the number is divided by 15 using the given information.

Calculation

To find the remainder when the number is divided by 15, we can use the fact that the remainder will be the same as when the number is divided by 45.

Given: - Divisor: 45 - Remainder: 21

We can express the remainder as: - 45a + 21, where 'a' is an integer.

Now, we need to find the equivalent expression for the remainder when divided by 15.

Equivalent Expression

To find the equivalent expression for the remainder when divided by 15, we can express the remainder in terms of 15.

The remainder when divided by 15 can be expressed as: - (45a + 21) = 15(3a) + 21

Therefore, the remainder when the number is divided by 15 will be 21.

This means that the remainder when the number is divided by 15 is also 21, based on the given information about the remainder when divided by 45.

This conclusion is based on the principles of modular arithmetic and the relationship between remainders when dividing by multiples of a given divisor.