The factors of 168 and the prime factors of 168 differ because hundred and sixty-eight is a composite number. Also, despite being closely related, the prime factors of 168 and the prime factorization of 168 are not exactly the same either. In any case, by reading on you can learn the answer to the question what are the factors of 168? and everything else you want to know about the topic.
What are the Factors of 168?
They are: 168, 84, 56, 42, 28, 24, 21, 14, 12, 8, 7, 6, 4, 3, 2, 1. These are all the factors of 168, and every entry in the list can divide 168 without rest (modulo 0). That’s why the terms factors and divisors of 168 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 168, as well as 1 are factors and divisors of 168.
Prime Factors of 168
The prime factors of 168 are the prime numbers which divide 168 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 168 divides the number 168 without any rest, modulo 0.
For 168, the prime factors are: 2, 3, 7. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 168 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 168
The prime factorization of 168 is 2 x 2 x 2 x 3 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 168 does not include the number 1, yet it does include every instance of a certain prime factor.
168 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 168 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 168, 84, 56, 42, 28, 24, 21, 14, 12, 8, 7, 6, 4, 3, 2, 1 and multiply these integers to obtain 168. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 168.
The prime factorization or integer factorization of 168 means determining the set of prime numbers which, when multiplied together, produce the original number 168. This is also known as prime decomposition of 168.
Besides factors for 168, frequently searched terms on our website include:
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To sum up:
The factors, the prime factors and the prime factorization of 168 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of hundred and sixty-eight are: 168, 84, 56, 42, 28, 24, 21, 14, 12, 8, 7, 6, 4, 3, 2, 1. The prime factors of hundred and sixty-eight are 2, 3, 7. And the prime factorization of hundred and sixty-eight is 2 x 2 x 2 x 3 x 7. Remember that 1 is not a prime factor of 168.
No matter if you had been searching for prime factorization for 168 or prime numbers of 168, you have come to the right page. Also, if you typed what is the prime factorization of 168 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 168 as a product of prime factors or list the factors of 168 will no longer pose a challenge to you.
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