Prime factorization of 212
Understand the Problem
The question is asking for the prime factors of the number 212, which involves determining which prime numbers multiply together to give the original number.
Answer
$2^2 \times 53$
Answer for screen readers
The prime factorization of 212 is $2^2 \times 53$.
Steps to Solve
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Start with the number
We begin by identifying the number whose prime factors we need to find, which is 212. -
Divide by the smallest prime number
The smallest prime number is 2. We check if 212 is divisible by 2: $$ 212 \div 2 = 106 $$ Since 212 is even, it is divisible by 2. Therefore, 2 is one of the prime factors. -
Repeat the process with the quotient
Now we take the quotient, 106, and check if it is divisible by 2 again: $$ 106 \div 2 = 53 $$ So, we add another 2 to our list of prime factors. -
Check if the quotient is prime
We now check 53 to see if it's a prime number:
- It is not divisible by 2 (not even).
- The next prime number is 3, but $5 + 3 = 8$, not divisible by 3.
- Finally, check 5. $53 \div 5$ does not yield an integer.
Since 53 has no divisors other than 1 and itself, it is a prime number.
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Compile the final list of prime factors
We have found that:
- The prime factors of 212 are 2, 2, and 53.
Thus, we can write the prime factorization as: $$ 212 = 2^2 \times 53 $$
The prime factorization of 212 is $2^2 \times 53$.
More Information
The number 212 is an even number, which makes it divisible by 2. The process of finding prime factors is foundational in number theory and has applications in areas such as cryptography.
Tips
- A common mistake is to overlook factors after the first prime division. Ensure to check whether the resulting quotient is prime as well.
- Another mistake is to assume a number is prime without checking divisibility by smaller prime numbers.
