The number "492" is a three-digit number with a unique combination of digits. In this analysis, we will explore various aspects of this number, including its prime factorization, divisibility rules, and mathematical properties.
Prime Factorization
To find the prime factorization of a number, we need to determine the prime numbers that multiply together to give the original number. For 492, we can start by dividing the number by the smallest prime number, which is 2:
492 ÷ 2 = 246
Continue dividing by 2 until we can no longer divide evenly:
246 ÷ 2 = 123
Now, we divide by the next prime number, 3:
123 ÷ 3 = 41
Since 41 is a prime number itself, we stop dividing. Therefore, the prime factorization of 492 is:
492 = 2^2 × 3 × 41
Divisibility Rules
The divisibility rules help us determine if a number is divisible by another number without performing the actual division. Let’s see how these rules apply to 492:
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Divisible by 2: A number is divisible by 2 if the last digit is even. Since the last digit of 492 is 2, which is even, 492 is divisible by 2.
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Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. In this case, 4 + 9 + 2 = 15, which is divisible by 3. Therefore, 492 is divisible by 3.
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Divisible by 4: A number is divisible by 4 if the last two digits form a number divisible by 4. The last two digits of 492 are 92, which is divisible by 4. Hence, 492 is divisible by 4.
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Divisible by 6: A number is divisible by 6 if it is divisible by both 2 and 3. Since 492 is divisible by 2 and 3, it is divisible by 6.
Mathematical Properties
- 492 is an even number because it is divisible by 2.
- The sum of the digits of 492 is 4 + 9 + 2 = 15.
- The digit sum of 492 is divisible by 3, making 492 a multiple of 3.
- The prime factorization of 492 is 2^2 × 3 × 41, which shows that it can be expressed as a product of prime numbers.
In conclusion, the number 492 has multiple mathematical properties, including being an even number, divisible by 2, 3, 4, and 6, as well as having a prime factorization of 2^2 × 3 × 41. These characteristics help us understand the mathematical nature of the number "492."
