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Ch 05 - Prime Time6th Ganita Prakash
Mathematical Multiples
What is the strict mathematical definition of a 'Multiple' of a number?
What is the strict mathematical definition of a 'Multiple' of a number?
DEFINITION
- Definition: A multiple of a number is the mathematical product obtained by multiplying that specific base number by any natural counting number ().
Boundary Conditions / Domain:
- Every number is strictly a multiple of exactly and itself.
- The list of multiples for any non-zero number is infinitely long.
Prism Memory Hook
Multiply to get Multiples.
Common Multiples
What mathematical condition defines a 'Common Multiple' between two or more distinct numbers?
What mathematical condition defines a 'Common Multiple' between two or more distinct numbers?
DEFINITION
- Definition: A numerical value that appears simultaneously in the list of multiples of two or more distinct base numbers.
- Example: is a common multiple of and because it perfectly satisfies both and .
Prism Memory Hook
A premium mnemonic for this topic is available in the Prism App.
Factors (Divisors)
What is the mathematical definition of a Factor (or Divisor) of a number, and what are its absolute minimum and maximum boundaries?
What is the mathematical definition of a Factor (or Divisor) of a number, and what are its absolute minimum and maximum boundaries?
DEFINITION
- Definition: Numbers that divide a given target number strictly exactly, leaving a remainder of precisely .
Boundary Conditions / Domain:
- The absolute smallest factor of any positive integer is strictly .
- The absolute largest geometric factor is strictly the number itself.
Prism Memory Hook
Factors fraction it exactly.
Also in this chapter
36 more cards to study in Prism
- 4Common Factors
- 5Perfect Number Definition
- 6Prime Numbers
- 7The Even Prime Exception
- 8Composite Numbers
- 9The Number 1 Boundary Trap
- 10Sieve of Eratosthenes Algorithm
- 11Twin Primes
- 12Co-prime Numbers
- 13Co-prime Trap: Prime Requirement
- 14First Common Multiple (LCM) of Co-primes
- 15Prime Factorisation
- 16Uniqueness of Prime Factorisation
- 17SOP: Repeated Division Algorithm (Prime Factorisation)
- 18SOP: Co-prime Verification via Prime Factors
- 19SOP: Divisibility Verification via Prime Factors
- 20Divisibility Test for 10
- 21Divisibility Test for 5
- 22Divisibility Test for 2 (Even Numbers)
- 23Divisibility Test for 4
- 24Divisibility Test for 8
- 25Composite Divisibility Intersection Rule
- 26Mental Math: Remainder of Division by 10
- 27Mental Math: Remainder of Division by 5
- 28Mental Math: Remainder of Division by 2
- 29Calculating the n-th Common Multiple
- 30Thread Art Full Connectivity Theorem
- 31Leap Year Century Boundary Condition
- 32Non-Zero Unit Digit Factoring Trap ($10^n$)
- 33Reversible Prime Pairs (Emirps) under 100
- 34Maximum Prime Gap Sequence (Under 100)
- 35The Doubling Primes Transformation
- 36Smallest 4-Digit Palindrome Divisible by 4
- 37Parity Summation Trap (Modulo 4)
- 38Minimizing Distinct Prime Products
- 39Prime Grid Intersection Algorithm
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6th Ganita Prakash
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