DP Further Mathematics HL Questionbank

• Syllabus

6.2

Sub sections and their related questions

\(\left. a \right|b \Rightarrow b = na\) for some \(n \in \mathbb{Z}\) .

• 18M.1.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 74 and 383.
• 18M.1.hl.TZ0.1b: Hence find integers s and t such that 74s + 383t = 1.

The theorem \(\left. a \right|b\) and \(\left. a \right|c \Rightarrow \left. a \right|(bx \pm cy)\) where \(x,y \in \mathbb{Z}\) .

• 18M.1.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 74 and 383.
• 18M.1.hl.TZ0.1b: Hence find integers s and t such that 74s + 383t = 1.

Division and Euclidean algorithms.

• 09M.1.hl.TZ0.4: Prove that \(3k + 2\) and \(5k + 3\) , \(k \in \mathbb{Z}\) are relatively prime.
• 13M.1.hl.TZ0.1a: (i)     Use the Euclidean algorithm to find gcd(\(6750\), \(144\)) . (ii)     Express your...
• 07M.1.hl.TZ0.4a: Use the Euclidean Algorithm to show that \(275\) and \(378\) are relatively prime.
• 16M.1.hl.TZ0.9a: Use the Euclidean algorithm to find \(\gcd (162,{\text{ }}5982)\).
• 18M.1.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 74 and 383.
• 18M.1.hl.TZ0.1b: Hence find integers s and t such that 74s + 383t = 1.

The greatest common divisor, gcd(\(a\),\(b\)), and the least common multiple, lcm(\(a\),\(b\)), of integers \(a\) and \(b\).

• 11M.1.hl.TZ0.4a: Prove that if \({\rm{gcd}}(a,b) = 1\) and \({\rm{gcd}}(a,c) = 1\) , then \({\rm{gcd}}(a,bc) = 1\) .
• 12M.1.hl.TZ0.2b: The positive integers \(M\) , \(N\) are such that \(\gcd (M,N) = 63\) and \(lcm(M,N) = 47502\) ....
• 18M.1.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 74 and 383.
• 18M.1.hl.TZ0.1b: Hence find integers s and t such that 74s + 383t = 1.

Prime numbers; relatively prime numbers and the fundamental theorem of arithmetic.

• 12M.1.hl.TZ0.2a: Express the number \(47502\) as a product of its prime factors.
• 18M.1.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 74 and 383.
• 18M.1.hl.TZ0.1b: Hence find integers s and t such that 74s + 383t = 1.