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- 5 = 1 - Ready Digital AB

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution: The prime factorization of 2048 is $2^{11}$, and 1024 is $2^{10}$. The LCM of two numbers is the product of the highest powers of all primes present. Thus, $ ext{LCM}(2048, 1024) = 2^{11} = 2048$. The answer is $oxed{2048}$.

📌 Question: What is the base-ten number represented by the base-eight number 315?

📌 Solution: Converting $315_8$ to decimal: $3 imes 8^2 + 1 imes 8^1 + 5 imes 8^0 = 3 imes 64 + 1 imes 8 + 5 imes 1 = 192 + 8 + 5 = 205$. The base-ten equivalent is $oxed{205}$.

📌 Question: How many of the 100 smallest positive integers are congruent to 3 mod 7?

📌 Solution: Numbers congruent to 3 mod 7 are $3, 10, 17, \ldots, 3 + 7k$. The largest such number $\leq 100$ satisfies $3 + 7k \leq 100 \Rightarrow k \leq rac{97}{7} pprox 13.857$. Thus, $k = 0, 1, \ldots, 13$, giving 14 numbers. The count is $oxed{14}$.

📌 Question: What is the greatest common divisor of 2025 and 1024?

📌 Solution: The prime factorization of 2025 is $3^4 imes 5^2$, and 1024 is $2^{10}$. Since there are no common prime factors, the GCD is 1. The answer is $oxed{1}$.

📌 Question: What is the remainder when $1^2 + 2^2 + \cdots + 15^2$ is divided by 13?

🔥 Popular Posts

\(3 + b = 1 \rightarrow b = -2\).
Substitute into \(a + b + c = 2\):
\(1 - 2 + c = 2 \rightarrow c = 3\).
Thus, \(a + b + c = 1 - 2 + 3 = 2\).
A cylindrical tank with a radius of 5 meters is filled with water to a...
Original volume: \(\pi \times 5^2 \times 10 = 250\pi\) cubic meters.
New radius: \(5 \times 1.2 = 6\) meters.
New volume: \(\pi \times 6^2 \times 10 = 360\pi\) cubic meters.
A sequence is defined by \(a_n = 3n^2 - 2n + 1\). Find the 10th term.
\(a_{10} = 3(10)^2 - 2(10) + 1 = 300 - 20 + 1 = 281\).

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