Name: Fundamental Theorem of Arithmetic
Uploaded: 2019-07-19
Duration: 5 min 4 s
Description: A number can be represented in the form of the Product of their Primes. This method is also called the Fundamental Theorem of Arithmetic. Watch the video to...

Question

State fundamental theorem of arithmetic.

Accepted Answer

Fundamental theorem of Arithmetic states that, a composite number is expressed in the form of the product of primes and this factorization is unique apart from the order in which the prime factor occurs.

In general, a composite number “ $a$ ” can be expressed as,

$a = p_{1} p_{2} p_{3} \dots \dots \dots \dots p_{n}$ , where $p_{1}, p_{2}, p_{3} \dots \dots \dots \dots p_{n}$ are the prime factors of $a$ written in ascending order, that is, $p_{1} \leq p_{2} \leq p_{3} \dots \dots \dots \dots \leq p_{n}$

Writing the primes in ascending order makes the factorization unique in nature.

Let us consider an example of $35$ which can be written as product of primes.

$35 = 7 \times 5$

State fundamental theorem of arithmetic.

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