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Home » \[ (x - 8)(x - 4) = 0 \] - Coaching Toolbox

\[ (x - 8)(x - 4) = 0 \] - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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

📌 Therefore, there are 14 integers in the first 100 positive integers that are congruent to 3 modulo 7.

📌 What is the smallest four-digit number that is divisible by both 8 and 9?

📌 To find the smallest four-digit number divisible by both 8 and 9, calculate the least common multiple (LCM) of 8 and 9. Since 8 and 9 are coprime, their LCM is:

📌 Now, identify the smallest four-digit number divisible by 72. The smallest four-digit number is 1000. Divide 1000 by 72:

📌 Thus, 1008 is the smallest four-digit number divisible by both 8 and 9.

📌 To compute the greatest common divisor (GCD), take the minimum exponent for each common prime factor in the prime factorizations.

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