Factor of an Integer

Elementary SchoolMiddle School

Definition

When you have a number the divides evenly into another one, and in this case, these numbers are integers. Integers are whole numbers and fractions do not count as integers. As an example, the factors of 25 equals to 1, 5, and 25. 1, 5, and 25 are all whole numbers and not fractional ones.

Worked examples

\(12 \div 3 = 4\)

Since 3 divides evenly into 12, we say 3 is a factor of 12.

Factors of \(18\): \(1, 2, 3, 6, 9, 18\)

Each of these integers divides 18 with no remainder.

Common mistakes

\(\frac{1}{2}\) is a factor of \(10\) because \(10 \div \frac{1}{2} = 20\) → Only integers like \(1, 2, 5, 10\) are factors of \(10\) Factors must be whole numbers; fractions are not factors of integers.
\(7\) is a factor of \(20\) because \(20 \div 7 \approx 2.86\) → \(7\) is not a factor of \(20\) because \(20 \div 7\) leaves a remainder A factor must divide evenly with zero remainder.
The only factors of \(16\) are \(2\) and \(8\) → All factors of \(16\) are \(1, 2, 4, 8, 16\) Don't forget 1 and the number itself — they are always factors.

Where you'll use it next

You'll use factors when simplifying fractions, finding greatest common factors and least common multiples, solving factoring problems in algebra, and working with divisibility and prime factorization.

Found in 1 StudyPug lesson

Prime Factorization: Mastering Division by Primes

8th Grade Math

Unlock the power of prime factorization with our step-by-step guide. Learn essential techniques, from factor trees to the ladder method, and boost your math prowess. Perfect for students of all levels!

8th Grade8th