Podcast
Questions and Answers
Explain why 1 is a factor of every number.
Explain why 1 is a factor of every number.
Because every number is divisible by 1 without leaving a remainder.
How can you determine if a number is a 'perfect number'?
How can you determine if a number is a 'perfect number'?
Find all the factors of the number, sum them, and if the sum equals twice the original number, it's a perfect number.
What is a key difference between factors and multiples of a number?
What is a key difference between factors and multiples of a number?
Factors are less than or equal to the number, while multiples are greater than or equal to the number.
Why is the number of factors of any given number always finite?
Why is the number of factors of any given number always finite?
Describe the relationship between a number and its multiples.
Describe the relationship between a number and its multiples.
Explain why prime factorization is a unique representation of a number.
Explain why prime factorization is a unique representation of a number.
What is the smallest composite number, and why is it composite?
What is the smallest composite number, and why is it composite?
How do you determine if a given number is a prime number?
How do you determine if a given number is a prime number?
What does it mean to say that 'every number is a multiple of itself'?
What does it mean to say that 'every number is a multiple of itself'?
Describe the process of finding the prime factorization of a number.
Describe the process of finding the prime factorization of a number.
Flashcards
What are factors?
What are factors?
Factors are numbers that divide evenly into another number.
Is 1 a factor of all numbers?
Is 1 a factor of all numbers?
1 is a factor of every number.
Is a number a factor of itself?
Is a number a factor of itself?
Every number is a factor of itself.
What are perfect numbers?
What are perfect numbers?
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What are multiples?
What are multiples?
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Size of multiples
Size of multiples
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Number of multiples
Number of multiples
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What are prime numbers?
What are prime numbers?
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What are composite numbers?
What are composite numbers?
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What is prime factorization?
What is prime factorization?
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Study Notes
Properties of Factors
- 1 is a factor of every number.
- A number is a factor of itself.
- A number's factor is an exact divisor of that number.
- Factors are less than or equal to the given number.
- The number of factors for a given number is finite.
Perfect Numbers
- When the sum of all factors equals twice the number, that number is a perfect number.
- Factors of 28 are 1, 2, 4, 7, 14, and 28.
- 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 x 28; the sum of factors of 28 equals twice the number 28.
Multiples
- Multiples are numbers obtained by multiplying a number by any integer.
- Multiples of 3 are 6, 9, 12, 15, 18, etc.
Properties of Multiples
- Every multiple of a number is greater than or equal to that number.
- The number of multiples for a given number is infinite.
- Every number is a multiple of itself.
Prime Numbers
- Numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
- 2, 3, 5, 7, etc., are examples of prime numbers.
Composite Numbers
- Numbers having more than two factors are called Composite Numbers.
- 4, 6, 8, etc., are examples of composite numbers.
Prime Factorisation
- When a number is expressed as a product of prime numbers, factorisation is called prime factorisation.
- Prime factorisation of 36 is 2×2×3×3.
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