The exponent of 3 in the prime factorization of 576 is

The prime factorisation of a number involves breaking it down into its smallest prime factors. To determine the exponent of 3 in the prime factorisation of 576, we perform the following steps:

1. Start with the number 576. Divide it by the smallest prime number, which is 2, repeatedly until it is no longer divisible by 2.
2. The continuous division results in:
   • 576 ÷ 2 = 288
   • 288 ÷ 2 = 144
   • 144 ÷ 2 = 72
   • 72 ÷ 2 = 36
   • 36 ÷ 2 = 18
   • 18 ÷ 2 = 9
3. At this point, 9 is not divisible by 2. Proceed to the next prime number, which is 3.
4. Divide 9 by 3 repeatedly:
   • 9 ÷ 3 = 3
   • 3 ÷ 3 = 1

Thus, the prime factorisation of 576 is:

576 = 2⁶ × 3²

In the prime factorisation of 576, the exponent of 3 is 2, as 3 appears as a factor raised to the power of 2.

Also Check: Factor of 36

Final Answer

The prime factorisation of 576 reveals that it consists of the prime number 2 raised to the power of 6 and the prime number 3 raised to the power of 2. Therefore, the exponent of 3 in the prime factorisation of 576 is 2.