The Factors of 7429 are the numbers which get multiplied and produce the result as 7429. Suppose multiplying 2 and 8, we get 16, i.e. 2 × 8 = 16 such that 2 and 8 are the factors of 16. Also, (2, 8) is called one of the factor pairs of 16. Similarly, we can find the factors of the number 7429. However, finding the factors for large numbers such as 7429 is not easy since it is difficult to identify the numbers which produce 7429 by multiplication. In this article, you will get the factors of 7429, how to find the factors of a number 7429 in pairs using different methods and prime factors of 7429 with detailed steps.

What are the Factors of 7429?

Also, we know that the factors for 7429 are the exact divisors of that number. The number 7429 is a composite number and hence it has more than two factors, that means it has factors other than 1 and 7429.

Generally, we can find the factors for any given number in two ways, namely division method and factor pair method.

How to Find the Factors of 7429?

Go through the steps given below to understand the process of finding the factors of 7429.

Step 1: First, write the number 7429 in your notebook.

Step 2: Find the two numbers, which on multiplication gives 7429, suppose 17 and 437, such as 17 × 437 = 7429.

Step 3: We know that 17 is a prime number which has only two factors, i.e. 1 and the number itself. So, we cannot factorize it further.

17 = 1 × 17

Step 4: Now, let’s try with different combinations of numbers in multiplication that produce the result as 7429, such as

19 × 391 = 7429

23 × 323 = 7429

Step 5: Therefore, factors of 7429 are: 1, 17, 19, 23, 323, 391, 437, and 7429.

Factors of 7429 by Division Method

As we know, factors are the exact divisors of the numbers. So we can also find the factors for 7429 by division method. Since 7429 is an odd number, it has only odd factors. Therefore, we will be checking with only odd numbers in this method.

7429 ÷ 1 = 7429 {remainder = 0, 1 and 7429 are factors}

7429 ÷ 3 = 2476.33 {remainder ≠ 0; not an exact divisor}

7429 ÷ 5 = 1485.8 {remainder ≠ 0; not an exact divisor}

7429 ÷ 7 = 1061.2857 {remainder ≠ 0; not an exact divisor}

7429 ÷ 9 = 825.444 {remainder ≠ 0; not an exact divisor}

7429 ÷ 11 = 675.3636 {remainder ≠ 0; not an exact divisor}

7429 ÷ 13 = 571.4615 {remainder ≠ 0; not an exact divisor}

7429 ÷ 15 = 495.266 {remainder ≠ 0; not an exact divisor}

7429 ÷ 17 = 437 {remainder = 0, 17 and 437 are factors}

7429 ÷ 19 = 391 {remainder = 0, 19 and 391 are factors}

7429 ÷ 21 = 353.7619 {remainder ≠ 0; not an exact divisor}

7429 ÷ 23 = 323 {remainder = 0, 23 and 323 are factors}

7429 ÷ 25 = 297.16 {remainder ≠ 0; not an exact divisor}

…

7429 ÷ 323 = 23

Factor of 7429 in Pairs

The factors of any number can be both positive and negative. To get the pair factors of 7429, multiply the 2 numbers in a pair to have the original number as 7429. Such numbers are tabulated below:

Therefore, the positive pair factors of 7429 are (1, 7429), (17, 437), (19, 391), (23, 323), (323, 23), (391, 19), (437, 17), and (7429, 1).

Also, the negative pair factors of 7429 are (-1, -7429), (-17, -437), (-19, -391), (-23, -323), (-323, -23), (-391, -19), (-437, -17), and (-7429, -1).

Below are the important facts about the factors of 7429.

• The total number of factors of 7429 is 8.
• The sum of factors of 7429 is 8640.
• As 7429 is an odd number, it has only odd factors.

Prime Factors of 7429

By prime factorization method, we can write the prime factors of 7429 as given below.

Step 1: The first step is to divide the number 7429 with the smallest prime number, i.e. 2.

7429 ÷ 2 = 3714.5

As we know, the factors cannot be a fraction, therefore, 2 is not the prime factor for 7429. So proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

7429 ÷ 3 = 2476.33

7429 ÷ 5 = 1485.8

7429 ÷ 7 = 1061.2857

7429 ÷ 11 = 675.3636

7429 ÷ 13 = 571.4615

7429 ÷ 17 = 437; 17 is a prime factor of 7429.

Step 2: Now, we divide 437 by 2.

437 ÷ 2 = 218.5

As we know, the factors cannot be a fraction, therefore, 2 is not the prime factor for 437.

Step 3: Now, proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

437 ÷ 3 = 145.66

437 ÷ 5 = 87.5

437 ÷ 7 = 62.4285

437 ÷ 11 = 39.7272

437 ÷ 13 = 33.6154

437 ÷ 17 = 25.7058

437 ÷ 19 = 23; 19 and 23 are prime numbers and hence, we cannot proceed with the division method.

Thus, the prime factorisation of 7429 can be expressed as 17 × 19 × 23.

Note:

The exponents in the prime factorization of 7429 are 1, 1, and 1. By adding one to each and multiplying them we get, (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Thus, 7429 has exactly 8 factors.

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