The prime factorization of 425 using exponents
The correct answer and explanation is:
The prime factorization of 425 using exponents is:
425 = 5² × 17
Explanation:
To determine the prime factorization of a number like 425, the goal is to express it as a product of prime numbers. A prime number is a number that can only be divided by 1 and itself. Let’s break down the process step by step.
- Start with 425:
The first step is to check if 425 is divisible by the smallest prime number, which is 2. Since 425 is an odd number, it is not divisible by 2. - Check divisibility by 3:
Next, check if 425 is divisible by 3. A simple rule is to add the digits of 425 (4 + 2 + 5 = 11) and see if the sum is divisible by 3. Since 11 is not divisible by 3, 425 is not divisible by 3. - Check divisibility by 5:
The next smallest prime number is 5. Since 425 ends in a 5, it is divisible by 5. Dividing 425 by 5 gives: 425÷5=85425 ÷ 5 = 85 This means 425 = 5 × 85. - Factor 85:
Now, take the factor 85. Again, since 85 ends in 5, it is divisible by 5. Dividing 85 by 5 gives: 85÷5=1785 ÷ 5 = 17 Now we have 425 = 5 × 5 × 17, or 5² × 17. - Prime check for 17:
Finally, check if 17 is a prime number. Since 17 is only divisible by 1 and itself, it is a prime number.
Thus, the prime factorization of 425 is 5² × 17. This expresses 425 as a product of primes, with the exponent showing that 5 is used twice in the factorization.