What Is the Smallest Factor of Any Number

Factors of 14

Factors of 14 are integers that can be divided evenly into 14. It has a total of 4 factors of which 14 is the biggest factor and the positive factors of 14 are 1, 2, 7, and 14. The sum of all factors of 14 is 24 and its factors in Pairs are (1, 14) and (2, 7).

• Factors of 14: 1, 2, 7 and 14
• Negative Factors of 14: -1, -2, -7 and -14
• Prime Factors of 14: 2, 7
• Prime Factorization of 14: 2 × 7 = 2 × 7
• Sum of Factors of 14: 24

1.	What Are the Factors of 14?
2.	How to Calculate the Factors of 14?
3.	Factors of 14 by Prime Factorization
4.	Factors of 14 in Pairs
5.	Smallest Composite Number

What Are the Factors of 14?

The factors of 14 are all the integers that divide 14 without leaving any remainder. 14 is an even composite number. To understand why it is composite, let us recall the definition of a composite number. A composite number is an integer that can be divided by another natural number, apart from itself and 1, without leaving a remainder.

Consider the number 19. It has only two factors which are 1 and 19. As it can only be divided by 1 and 19 completely, it is prime. Let's take the example of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Now, let's find the numbers that completely divide 14. The numbers are 1, 2, 7, and 14.

Important Notes

• 1 is the smallest factor of every number.

• 14 is a non-perfect square number. Thus, it will have an even number of factors. This property holds for every non-perfect square number.

How to Calculate the Factors of 14?

• Let's begin calculating the factors of 14, starting with the smallest whole number, i.e. 1. On dividing 14 by 1, the remainder is 0. Hence 1 is the factor of 14.
• The next number is 2. Now, 14÷2 = 7, the remainder is 0. Hence 2 is the factor of 14.
• Proceeding in a similar manner we get, 14÷7 = 2 and 14÷14=1.

Thus, the factors of 14 are 1, 2, 7, and 14.

Explore factors using illustrations and interactive examples:

• Factors of 140 - Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70 and 140.
• Factors of 144 - Factors of 144 are1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
• Factors of 41 - The factors of 41 are 1, and 41.
• Factors of 147 - The factors of 147 are 1, 3, 7, 21, 49, and 147.

Factors of 14 in Pairs

The pair of numbers that give 14 when multiplied is known as the factor pairs of 14.

Following are the factors of 14 in pairs.

Product form of 14	Pair factor
1 x 14 = 14	(1,14)
2 x 7 = 14	(2,7)

Let's take a look at the negative pair factors of 14. If we consider negative integers, then both the numbers in the pair factors have to be negative. It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number.

Thus, we can have negative factor pairs of 14 as (-1,-14) and (-2,-7).

Factors of 14 by Prime Factorization

Prime factorization means to express a composite number as the product of its prime factors.

To get the prime factorization of 14, we divide it by its smallest prime factor which is 2.

14/2 = 7

Now, 14 is divided by the remaining prime factors 3, 5, 7, 11, and 13.

14 is only divisible by 7 and we get the quotient as 2.

14/7 = 2

Thus, 14 has 2 prime factors.

Now that we have done the prime factorization of 14, we can multiply it and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.

Solved Examples

1. Example 1:When a teacher asked a question, some students raised their hands. But instead of raising one hand, each student raised both their hands. If there are 14 hands in total, how many students raised their hands?

   Solution

   The number of hands raised = 14

   To find the number of students who raised their hands, we have to divide 14 by 2 because each student raised both hands.

   Number of students = 14/2 = 7

   Therefore, 7 students raised their hands.

2. Example 2:James wanted to count all the positive and negative factors of 14. Help him count them.

   Solution

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

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

   Hence, the total number of factors of 14 is 8.

3. Example 3: How many factors are there for 14?

   Solution:

   The factors of 14 are 1, 2, 7, 14. Therefore, 14 has 4 factors.

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FAQs on Factors of 14

What are the Factors of 14?

The factors of 14 are 1, 2, 7, 14 and its negative factors are -1, -2, -7, -14.

What is the Greatest Common Factor of 14 and 10?

The factors of 14 and 10 are 1, 2, 7, 14 and 1, 2, 5, 10 respectively.

Common factors of 14 and 10 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 14 and 10 is 2.

What numbers are the Pair Factors of 14?

The pair factors of 14 are (1, 14), (2, 7).

What is the Sum of the Factors of 14?

Since all factors of 14 are 1, 2, 7, 14 therefore, the sum of its factors is 1 + 2 + 7 + 14 = 24.

What are the Common Factors of 14 and 5?

Since the factors of 14 are 1, 2, 7, 14, and factors of 5 are 1, 5. Hence, 14 and 5 have only one common factor which is 1. Therefore, 14 and 5 are co-prime.

What Is the Smallest Factor of Any Number

Source: https://www.cuemath.com/numbers/factors-of-14/

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