NOVEMBER 08, 2023

Factors of a number refer to the numbers that divide the given number without leaving a remainder. In this blog, we will explore the factors of 14 and understand their properties.

The factors of 14 are 1, 2, 7, and 14.

To find the factors of 14, we can follow these steps:

Determine the criteria for judging whether a number is a factor. A number is a factor of 14 if it divides 14 without leaving a remainder.

List all the numbers starting from 1 up to the given number, which is 14 in this case.

Use each number as a divisor and verify whether it is a factor by dividing 14 by the number. If the division results in an integer value, then the number is a factor of 14.

Finally, collect all the numbers that satisfy the criteria and are factors of 14.

Let's now provide a concise step-by-step solution using math expressions.

Determine the criteria: A number is a factor of 14 if it divides 14 without leaving a remainder.

List all the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

Verify each number as a factor:

- 1 is a factor of 14 since 14 ÷ 1 = 14.
- 2 is a factor of 14 since 14 ÷ 2 = 7.
- 3 is not a factor of 14 since 14 ÷ 3 = 4.6667 (not an integer).
- 4 is not a factor of 14 since 14 ÷ 4 = 3.5 (not an integer).
- 5 is not a factor of 14 since 14 ÷ 5 = 2.8 (not an integer).
- 6 is not a factor of 14 since 14 ÷ 6 = 2.3333 (not an integer).
- 7 is a factor of 14 since 14 ÷ 7 = 2.
- 8 is not a factor of 14 since 14 ÷ 8 = 1.75 (not an integer).
- 9 is not a factor of 14 since 14 ÷ 9 = 1.5556 (not an integer).
- 10 is not a factor of 14 since 14 ÷ 10 = 1.4 (not an integer).
- 11 is not a factor of 14 since 14 ÷ 11 = 1.2727 (not an integer).
- 12 is not a factor of 14 since 14 ÷ 12 = 1.1667 (not an integer).
- 13 is not a factor of 14 since 14 ÷ 13 = 1.0769 (not an integer).
- 14 is a factor of 14 since 14 ÷ 14 = 1.

Collect the factors: The factors of 14 are 1, 2, 7, and 14.

The pair factors of 14 are (1, 14) and (2, 7). These pairs are obtained by multiplying two factors of 14 that result in 14.

The negative pair factors of 14 are (-1, -14), (-2, -7), (1, -14), and (2, -7). These pairs are obtained by multiplying a factor of 14 with its negative counterpart.

Prime factorisation of a number involves expressing it as a product of prime numbers. The prime factorisation of 14 is 2 × 7. This means that 2 and 7 are the prime factors of 14, and when multiplied together, they give the original number.

Example: Find the factors of 14. Solution: The factors of 14 are 1, 2, 7, and 14.

Example: Determine the pair factors of 14. Solution: The pair factors of 14 are (1, 14) and (2, 7).

Example: What is the prime factorisation of 14? Solution: The prime factorisation of 14 is 2 × 7.

In mathematics, factors are numbers that divide a given number without leaving a remainder. They play a crucial role in various mathematical concepts, such as prime numbers, composite numbers, and factorization.

In mathematics, factors are often represented using the multiplication symbol (×) or a dot (·). For example, the factors of 14 can be represented as 1 × 14, 2 × 7, or 1 · 14, 2 · 7.

There are two types of factors: prime factors and composite factors. Prime factors are numbers that are only divisible by 1 and themselves, while composite factors have additional factors apart from 1 and themselves.

**Question: Factors of 14?**
Answer: The factors of 14 are 1, 2, 7, and 14.

In conclusion, the factors of 14 are 1, 2, 7, and 14. We have explored their properties, pair factors, prime factorisation, and provided solved examples. Factors are essential in mathematics and have various applications in different mathematical concepts.