In the division of integers, there are only two situations: divisible and non-divisible. When it is not divisible, it will produce a remainder, so the remainder problem is very important in primary school mathematics.

Remainder operation:

A mod b = c means "integer a is divided by integer b, and the remainder is c".

Calculation formula of remainder:

Where is the rounding operator? Rounding down operation, called Floor in English, is represented by mathematical symbols.

For example:? 3.476? =3,? 6.7546? =6,? -3. 14 159? =-4,

Example 1: 5 120 is divided by a two-digit number, and the remainder is 64. Find this two-digit number.

Analysis and solutions:

According to the property (2), divisor × quotient = dividend-remainder.

5 120-64=5056, which should be an integer multiple of the divisor. 5056 is decomposed into prime factors, and 5056=64×79 is obtained.

According to the property (1), the divisor should be greater than 64, then the divisor is a two-digit number, and the divisor is between 67 and 99.

The divisor of 5056 is only 79, so this two-digit number is 79.