Podcast
Questions and Answers
What does it mean if a ∤ b?
What does it mean if a ∤ b?
- b is a divisor of a
- a does not divide b (correct)
- a is a factor of b
- a is a multiple of b
Which notation represents 'a divides b'?
Which notation represents 'a divides b'?
- a∤b
- b∤a
- a|b (correct)
- b|a
According to the Division Algorithm, what does 'a = d ×q + r' signify?
According to the Division Algorithm, what does 'a = d ×q + r' signify?
- Expression for division (correct)
- Expression for multiplication
- Expression for addition
- Expression for subtraction
Which property states that if a | b and a | c, then a | (b + c)?
Which property states that if a | b and a | c, then a | (b + c)?
If 4 | 64 and 8 | 64, then what can be inferred from this?
If 4 | 64 and 8 | 64, then what can be inferred from this?
Flashcards are hidden until you start studying
Study Notes
Divisibility Notation and Concepts
-
The notation ( a \nmid b ) indicates that ( a ) does not divide ( b ) evenly, meaning there is a remainder when ( b ) is divided by ( a ).
-
The notation for "a divides b" is represented as ( a \mid b ), which means that there exists an integer ( k ) such that ( b = a \times k ).
Division Algorithm
- The Division Algorithm states that for any integers ( a ) and ( d ) (where ( d > 0 )), there exist unique integers ( q ) (quotient) and ( r ) (remainder) such that ( a = d \times q + r ) with ( 0 \leq r < d ).
Properties of Divisibility
- The additive property of divisibility states that if ( a \mid b ) and ( a \mid c ), then ( a \mid (b + c) ). This means if ( a ) divides both ( b ) and ( c ), it also divides their sum.
Inference from Divisibility
- If ( 4 \mid 64 ) and ( 8 \mid 64 ), it can be inferred that both 4 and 8 divide 64 without remainder, confirming their status as divisors of 64.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
