Prime factorisation of 90 is

General
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prime factorisation of 90 is

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What is the prime factorization of 90?

Answer:

The prime factorization of a number is the process of breaking it down into its basic building blocks or prime numbers. A prime number is a number greater than 1 that has no divisors other than 1 and itself.

For the number 90, we can find its prime factorization by following these steps:

  1. Start with the smallest prime number, which is 2.

    • Check if 90 is divisible by 2. Since 90 is even, it is divisible by 2.
    • Divide 90 by 2:
      [
      90 \div 2 = 45
      ]
    • So, the first prime factor is 2.

  2. Move to the next smallest prime number, which is 3.

    • Check if 45 is divisible by 3. Since the sum of the digits (4 + 5 = 9), and 9 is divisible by 3, 45 is also divisible by 3.
    • Divide 45 by 3:
      [
      45 \div 3 = 15
      ]
    • Hence, the next prime factor is 3.

  3. Continue with the prime number 3 (since 15 is also divisible by 3).

    • Divide 15 by 3:
      [
      15 \div 3 = 5
      ]
    • This gives another factor of 3.

  4. Now we are left with 5, which is itself a prime number.

Thus, the prime factorization of 90 is:

[
90 = 2 \times 3 \times 3 \times 5
]

This can also be written using exponents for any repeated factors:

[
90 = 2 \times 3^2 \times 5
]

So, the prime factors of 90 are: 2, 3, and 5.