Question

What is the prime factorization of 144?

Answer 1

Answer:

Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written 144 = (2^4) x (3^2). 144 is the largest clue that appears in the FIND THE FACTORS 1 – 12 puzzles. For the puzzles in which it is a clue, always use 12 x 12 as the factors.

Answer 2

The prime factorization of 144 is 144 = 2 × 2 × 2 × 2 × 3 × 3.

Prime Factorization:

• A number is factored using prime numbers, or primes, in the process known as prime factorization.
• 2, 3, 5, 7, 11, 13, 17, and so forth are the first few prime numbers.
• When these prime numbers are multiplied by any natural integer, composite numbers are created.
• The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1.

In this way, we can find the prime factorization of 144.

The smallest prime which can divide 144 is 2 ⇒ 144 ÷ 2 = 72.

The smallest prime which can divide 72 is 2 ⇒ 72 ÷ 2 = 36.

The smallest prime which can divide 36 is 2 ⇒ 36 ÷ 2 = 18.

The smallest prime which can divide 18 is 2 ⇒ 18 ÷ 2 = 9.

The smallest prime which can divide 9 is 3 ⇒ 9 ÷ 3 = 3.

The smallest prime which can divide 3 is 3 ⇒ 3 ÷ 3 = 1.

We got reminder 1, and cannot proceed further.

Hence, the prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3

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