First, we need to know what an integer is. Integer is a number without decimal part, including positive integer, negative integer and zero. For example, -3, -2,-1, 0, 1, 2, 3 and so on are all integers.
A prime number is a natural number with only two positive factors (1 and itself), that is, only two different natural numbers can divide it exactly. For example, 2, 3, 5, 7, 1 1 are prime numbers.
Factorization is the process of decomposing an integer into the product of several prime numbers. For example, 12 can be decomposed into 2*2*3.
Congruence is an equivalent relationship. If two integers A and B satisfy that a-b is a multiple of integer M, then we say that A and B are congruent. For example, 10 and 12 are congruent, because 10- 12=-2 is a multiple of 2.
A common multiple is a common multiple of two or more integers. For example, common multiples of 6 and 8 are 24, 48, 72, etc.
The greatest common divisor is the greatest common divisor of two or more integers. For example, the greatest common divisor of 12 and 16 is 4.
The least common multiple is the least common multiple of two or more integers. For example, the least common multiple of 12 and 16 is 48.
In number theory, we will also study some complicated problems, such as Fermat's last theorem and Goldbach's conjecture. These problems involve deeper mathematical theories and methods, such as algebra, geometry, probability and so on.