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Home » Altitude to leg \(b = 8\): - Appfinity Technologies

Altitude to leg \(b = 8\): - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\text{LCM} = 2^3 \cdot 3^1 = 8 \cdot 3 = 24
Therefore, the least common multiple is \(\boxed{24}\).
Question: What is the smallest prime factor of 77?
Solution: To find the smallest prime factor of 77, we test divisibilit...
77 is odd, so it is not divisible by 2.
Sum of digits of 77 is \( 7 + 7 = 14 \), which is not divisible by 3,...
The last digit is not 0 or 5, so 77 is not divisible by 5.
Check divisibility by 7: \( 77 \div 7 = 11 \), which is an integer.
Thus, 77 is divisible by 7, and since 7 is a prime number, it is the s...
Therefore, the smallest prime factor is \(\boxed{7}\).

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\div 7 = 7 \text{ remainder } 6 \Rightarrow 55 \equiv 6 \pmod{7}
\Rightarrow 55^2 \equiv 6^2 = 36 \equiv 1 \pmod{7}
Alternatively, $ 3025 \div 7 = 432 \text{ remainder } 1 $, so $ 3025 \...
Therefore, the remainder is $ \boxed{1} $.
Question: What is the greatest common divisor of $ 2^{12} - 1 $ and $...
Solution: We use the identity:
\gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a,b)} - 1
Here, $ a = 12 $, $ b = 18 $, so $ \gcd(12, 18) = 6 $.
Thus,
\gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = 63

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