# Number Theory Solved Problems

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A Brief Introduction To Number Theory Number theory is the branch of mathematics that studies integers, which are all the whole numbers on either side of the number line.

Number theory looks at specific properties of integers and seeks patterns in the ways different types of numbers are distributed or related to each other.

The prime factorisation of the integers is a central point of study in number theory and can be visualised with this Ulam spiral variant.

Number theory seeks to understand the properties of integer systems like this, in spite of their apparent complexity.

A Couple Of Simple Number Theory Problems And Solutions Many basic number theory problems relate to factoring.

## Number Theory Solved Problems

Following are a couple of examples: Problem: You have a quantity of cookies.

Solution: The answer is 12 because 2, 3, and 4 are all factors of 12, and 12 is the lowest common multiple of those numbers.

Problem: Which of the following numbers can not be divided into any smaller equal groups: 5106, 5281, or 5751?

All numbers except 0 and 1 have at least two factors: 1 and the number itself. The number 100, for example, has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Prime numbers are a special set of numbers that have only 2 distinct factors: 1 and the number itself.