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Methods of Finding the Factors of 29

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Last updated date: 16th May 2024
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An Introduction to the Factors of 29

A factor pair of 29 is the number that yields a result of 29 when two numbers are multiplied together. A factor of 29 will divide it equally. The factors of 29 cannot be of a fractional or decimal value. There are a total of 2 factors of 29. Thus, the factors are 1 and 29. Multiples occur when 29 is multiplied by consecutive natural numbers. The sum of all factors of 29 is 30. The pair factor of 29 is \[(1,29)\], where 29 is the prime number. In this article, let us learn how to find the factors of 29.


Factors of an Integer

A factor is an integer that is divided by the original number into equal parts without the remainder. Every number greater than one has at least two factors. Another factor is obtained if a number is divided by a factor. The two factors are referred to as factor products. The product of every factor pair corresponds to the number. The first factor pair is always 1 and counts itself.

Examples:

  • Factors of 5 are 1 and 5.

  • Factors of 10 are 1, 2, 5, and 10.


What are the Factors of 29?

There are only 2 factors for prime numbers, which are 1 and itself. Therefore, the only ways to divide these integers without leaving a remainder are by 1 and the number itself. 29 is a prime number, which means it has only 2 factors. So, the factors of 29 are 1 and 29.


How to Find the Factors of 29?

The numbers that divide exactly by 29 without leaving a remainder are known as the factors of 29. That is, the factors are those numbers that divide 29 exactly. 

\[29\div 1=29 \\ 29\div 29=1\]

We can see that the number 29 is divisible by 1 and 29. As a result, all of these integers are called the factors of 29.


Definition of Prime Factorization

Prime factorization is defined as the process of determining a number’s prime factors so that the original number is evenly divided by these factors because a composite number includes more than two elements. Thus, this method applies only to composite numbers instead of prime numbers.

Example of prime factorization:

8 is \[2\times 2\times 2\]


Prime Factorization of 29

The term "prime factorization" refers to representing a number as the product of its prime factors. 29 is a prime number, which means it has only 2 factors. So, the factors of 29 are 1 and 29. Thus, the prime factor of 29 is \[1\times 29\].


Pair Factors of 29

The only divisors that divide 29 without leaving a remainder are 29 and 1, calling them the factors of 29. Pair factors may be positive or negative, but they cannot be a fraction or a decimal. In pairs, the factors of 29 are \[(1,29)\] and \[(-1,-29)\].


Interesting Facts

  • A prime number and a composite number have a common factor, which is 1.

  • If the pair factor's numbers are composite numbers, divide them into their prime factors before expressing the result as the product of the prime factors.

  • One is the common factor of two prime numbers.


Solved Important Questions

1. Can you identify the number that results in 29 when multiplied by (-1)?

Ans: To determine this, we must divide 29 by \[-1\]\[=29\div -1=-29\]. Thus, the number that results in 29 when multiplied by \[-1\] is \[-29\].


2. What are the factors of 29 and the greatest factor of 129?

Ans: A factor of 29 will divide 29 equally. Hence, the factors of 129 are 1, 3, 43, and 129. The greatest factor of 129 is 129.


3. Find out the common factors of 29 and 39.

Ans: The common factor is the common number that divides each of two or more numbers.

The factors of 29 are given by 1, 29.

The factors of 39 are given by 1, 3, 13, and 39.

Hence, the common factor of 29 and 39 is 1.


Conclusion

The method for calculating the factors of 29 has been discussed in this article. 1 and 29 are the factors of 29. \[1\times 29\] is the prime factorisation of 29, where 29 is the prime number. Thus, the pair factors of 29 are \[(1,29)\] and \[(-1,-29)\].


Practice Questions

1. Is 29 a composite or a prime number?

  1. Prime number

  2. Composite number


2. Sum of the factors of 89 is____.

  1. 70

  2. 80

  3. 90

  4. 100


3. How many factors does a prime number have?

  1. 1

  2. 4

  3. 3

  4. 2


Answers

1. Option A

2. Option C

3. Option D

FAQs on Methods of Finding the Factors of 29

1. Write all the factors of 29.

A factor of 29 will divide 29 equally. Those factors cannot be of a fractional or decimal value. The pair factor of 29 is \[(1,29)\], where 29 is the prime number. 29 is a prime number, which means it has only 2 factors. So, the factors of 29 are 1 and 29. Thus, the prime factorisation of 29 is \[1\times 29\].

2. Differentiate Prime numbers and Composite numbers.


Prime Numbers

Composite Numbers

There are only 2 factors for prime numbers, which are 1 and itself.

There are more than two factors for composite numbers.

The only ways to divide these integers without leaving a remainder are by 1 and the number itself.

It can be divided by at least one positive integer in addition to being divided by 1 and the number itself.

Factors of 29 are 1 and 29.

Factors of 38 are 1, 2, 19, and 38.

Prime numbers are 2, 3, 5, 7, 11, 13, ...

Composite numbers are 4, 6, 8, 10, 12, 14, …


3. Write the pair factors of 150.

The positive pair factors of 150 are \[\left( 1,150 \right),~\text{ }\left( 2,\text{ }75 \right),\text{ }\left( 3,\text{ }50 \right),\text{ }\left( 5,\text{ }30 \right),\text{ }\left( 6,\text{ }25 \right)\] and \[\left( 10,\text{ }15 \right)\].


And also, the negative pair factors are \[\left( -1,-150 \right),~\left( -2,\text{ }-75 \right),\text{ }\left( -3,\text{ }-50 \right),\text{ }\left( -5,\text{ }-30 \right),\text{ }\left( -6,\text{ }-25 \right)\] and \[\left( -10,\text{ }-15 \right)\].