Find the prime factored form of the number.
275
A) $5 ^ { 2 } \cdot 11$
B) $5 ^ { 3 } \cdot 11$
C) $25 \cdot 11$
D) $25 ^ { 2 } \cdot 11$

Question

Quizplus · Accepted Answer

We can begin by dividing 275 by the smallest prime number, 2. We find that 2 does not divide 275, so we move on to the next smallest prime number, which is 3. Again, 3 does not divide 275, so we move on to 5. We find that 5 does divide 275, yielding a quotient of 55. We continue with the prime factorization of 55 by dividing it by 5, which gives us 11. Since 11 itself is a prime number, we are done with the prime factorization. Putting it all together, we have:

275 = 5 × 55
55 = 5 × 11

Therefore, the prime factorization of 275 is:

275 = 5 × 5 × 11 = 5^2 × 11

So, the answer is A) $5 ^ { 2 } \cdot 11$.

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Find the Prime Factored Form of the Number $5 ^ { 2 } \cdot 11$