find the prime factor by breaking by breaking down into smaller factors no are 32,45,468,522
The correct answer and explanation is:
Let’s break down the prime factors for each of these numbers:
1. 32:
- Start with dividing by 2, the smallest prime.
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Thus, the prime factorization of 32 is: 2 × 2 × 2 × 2 × 2 or 2^5.
2. 45:
- Start by dividing by 3, the smallest prime.
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Thus, the prime factorization of 45 is: 3 × 3 × 5 or 3^2 × 5.
3. 468:
- Start by dividing by 2.
468 ÷ 2 = 234
234 ÷ 2 = 117 - Now divide by 3.
117 ÷ 3 = 39
39 ÷ 3 = 13 - Now, 13 is a prime number.
Thus, the prime factorization of 468 is: 2 × 2 × 3 × 3 × 13 or 2^2 × 3^2 × 13.
4. 522:
- Start by dividing by 2.
522 ÷ 2 = 261 - Now divide by 3.
261 ÷ 3 = 87
87 ÷ 3 = 29 - 29 is a prime number.
Thus, the prime factorization of 522 is: 2 × 3 × 3 × 29 or 2 × 3^2 × 29.
Explanation:
Prime factorization is the process of breaking a number down into the prime numbers that multiply together to give the original number. Prime numbers are integers greater than 1 that are divisible only by 1 and themselves.
To factorize a number, we begin by testing divisibility by the smallest primes (starting with 2) and continue dividing by the primes until all factors are prime. In the case of even numbers like 32 and 468, the number is divisible by 2 repeatedly. For other numbers, such as 45, we use primes like 3 or 5 as divisibility rules apply (e.g., 3 divides a number if the sum of its digits is divisible by 3).