90 as a product of prime factors
Understand the Problem
The question is asking for the prime factorization of the number 90, which means expressing it as a product of its prime factors.
Answer
The prime factorization of 90 is $2 \cdot 3^2 \cdot 5$.
Answer for screen readers
The prime factorization of 90 is $2 \cdot 3^2 \cdot 5$.
Steps to Solve
- Start with the number 90
Begin by writing down the number, which we want to factor: $$90$$
- Divide by the smallest prime number
The smallest prime number is $2$. Check if $90$ is divisible by $2$: $$90 \div 2 = 45$$
Since the division is whole, we have found our first prime factor, which is $2$.
- Continue factoring with the next smallest prime number
Now take the result, $45$, and check if it's divisible by the next smallest prime number, $3$: $$45 \div 3 = 15$$
So, we identify $3$ as another prime factor.
- Factor the result again if possible
Next, we look at $15$. Check if $15$ is divisible by $3$ again: $$15 \div 3 = 5$$
Again, we find another prime factor, which is $3$.
- Factor the last result
Now we are left with $5$. Since $5$ is a prime number, we stop here.
- Collect all prime factors
Together, the prime factors we found are $2$, $3$, $3$, and $5$. We can express this as: $$90 = 2 \cdot 3^2 \cdot 5$$
The prime factorization of 90 is $2 \cdot 3^2 \cdot 5$.
More Information
The prime factorization helps understand the building blocks of a number. This is particularly useful in areas such as number theory and simplifying fractions. Prime factorization can also aid in finding the greatest common divisor (GCD) and least common multiple (LCM) of other numbers.
Tips
- Forgetting to check divisibility by smaller prime numbers systematically.
- Misidentifying a non-prime number as a prime factor.
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