Factors of 29 Using Prime Factorization
What are the Factors of 29?
The factors of 29 will be divisors which divide the number 29 exactly, leaving zero as the remainder. In this article, we will learn how we can find the list of all factors, prime factors and factor pairs of 29. Factors can be negative as well as positive.
Factors | Factors pairs | Prime factor |
|---|---|---|
1 , 29 | (1, 29) | 29 |
List of Factors of 29
To find out the total number of factors of 29, we need to do a divisibility test.
Divisor | Is the number a factor of 29? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all numbers | 1 \(\times\) 29 = 29 |
2 | No, 29 is odd | —------ |
3 | No, 2 + 9 = 11 is not divisible by 3 | —------ |
4 | No, as 29 \(\div\) 4 = 7 and the remainder = 1 | —------ |
5 | No, the ones digit is neither 0 nor 5 | —------ |
6 | No, 29 is neither divisible by 2 nor with 3 | —------ |
7 | No, as 29 \(\div\) 7 = 4 and the remainder = 1 | —------ |
8 | No, as 29 \(\div\) 8 = 3 and the remainder = 5 | —------ |
9 | No, Since 29 is not divisible by 3 | —------ |
10 | No, as 29 \(\div\) 10 = 2 and the remainder = 9 | —------ |
11 | No, as 29 \(\div\) 11 = 2 and the remainder = 7 | —------ |
We can keep checking the division of 29 till we reach 29 itself. This will tell us that none of the numbers divide 29 completely, except 1 and 29 itself. This suggests that 29 is a prime number with only two factors, 1 and 29.
Hence, the list of factors of 29 are 1 and 29.
Factor Pairs of 29
Positive factor of 29 | Positive factor pair of 29 |
|---|---|
1 \(\times\) 29 = 29 | (1, 29) |
The Prime Factor of 29
29 = 1 \(\times\) 29
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Rapid Recall
29 has only two factors, 1 and 29 itself.
Solved Factors of 29 Examples
Example 1: You want to organize 29 coins from your collection into a rectangular array on a table for an event at school. How many different arrays can you make?
Solution:
To find the number of arrays, find the number of factor pairs of 29. There is only one factor pair of 29, which is (1, 29). You can use each factor pair to make 2 arrays.
So, there are two ways to organize the coins in a rectangular array:
(a) One row and 29 columns.
(b) One column and 29 rows.
Example 2: Find the five positive multiples of 29.
Solution:
The first five positive multiples of 29 are:
1 \(\times\) 29 = 29
2 \(\times\) 29 = 58
3 \(\times\) 29 = 87
4 \(\times\) 29 = 116
5 \(\times\) 29 = 145
Example 3: Find the factors of 58.
Solution:
The factors of 58 are 1, 2 and 29.
No, factors must be less than the number itself. The number of factors of any number is finite.
The factors of any number will be divisors that divide the number exactly, leaving no remainder.
The prime factor will be a factor that is a prime number itself.
Example:
The factors of 45 are 1, 3, 5, 9, 15 and 45
The numbers written above are known as the factors of 45, but 3 and 5 are prime numbers, and they are the prime factors of 45.
The prime factors of 29 are 1 and 29.
The prime factors of 31 are 1 and 31.
The common factor of 29 and 31 is 1, but 1 is not a prime number.
So, there is no common prime factor between 29 and 31 .
29 and 31 are also called twin prime numbers.
The prime factors of 45 are 1, 3, 5, 9, 15 and 45
The prime factors of 65 are 1, 5, 13 and 65
The common factors of 45 and 65 are 1 and 5, but 1 is not a prime number.
So, there is one common prime factor of 45 and 65, which is 5 .