Question

Find the canonical decomposition of 2520

Answer 1

Question :- Find the canonical decomposition of 2520 ?

Solution :-

canonical decomposition :-

Let N is a Natural number . So, canonical decomposition of N will be :-

• N = a^p * b^q * c^r __________
• Here, a , b and c are distinct Prime numbers.
• Also, a < b < c .
• Or, we can say that prime factors are listed in numerical orders.
• p , q and r are positive integers .

First we will find prime factors of 2520 .

→ 2520 = 2 * 2 * 2 * 3 * 3 * 5 * 7

So,

→ 2520 = 2³ * 3² * 5 * 7

Here, as we can see :-

• 2, 3 , 5 and 7 are distinct prime numbers.
• Also, 2 < 3 < 5 < 7.
• Powers are Positive integers.

Therefore,

→ canonical decomposition of 2520 = 2³ * 3² * 5 * 7 (Ans.)