Write all factors of the following number 729.

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1,2,3,5,7,11,13

2,7,11

1,3,9,27,81,243

1,2,3,9,27,81

answer is C.

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Detailed Solution

Concept- To determine the 729 variables. We must first determine whether 729 can be divided into prime numbers and identify the prime factors. Once we have all the primary factors, we must combine them in as many ways as we can to produce the factors.
Before we attempt to answer the issue, let's define what a factor of any integer is.
A number is a factor of another number if it divides that other number exactly and without leaving any remnant. For example, if x divides y with a remainder of 0, then x is a factor of y.
Let's look for a factor of 10 as an illustration.
We know that the number 10 may be divided by 1, 2, and 5 with a remainder of 0, and that the number itself is a factor.
Thus, 1, 2, 5, and 10 are the factors of 10.
Finding the factors of 729 is now the task at hand. Always keep in mind that 729 is a perfect square because it has all odd-numbered components in count

.
We are aware that the common elements among all numbers are 1 and the number itself. Therefore, the elements of 729 must be 1 and 729.
Then, according to the divisibility test, 729 can be divided only by the prime number 3.
Using 729's prime factorization, we obtain

Therefore, 729 can be written as

. Therefore, these six threes are joined in every way possible, and the resulting goods are provided by,
Question Image

So, we got that the factors of 729 are 1,3,9,27,81,243
Hence, option 3 is correct.

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