Factors/Multiples (4) Flashcards
Prime number
POSITIVE integer with two factors (only itself and 1)
2 is the only…
even prime. And lowest prime number
Any number that isn’t prime, can be expressed as…
The product of primes
Factors
Positive integers that can divide N into another integer
Multiples
Integers that result from multiplying N by other integers (INCLUDING ZERO)
Zero characteristics
It is an even integer, but neither positive or negative. It is a multiple of everything.
1 characteristics
It is not a prime number (it has only one factor, itself). It is a prime of everything (don’t forget when counting possible factors)
If a number has an odd number of factors….
It is a perfect square (factors, not prime factors)
Factors are…. multiples are…
Finite, infinite
/ 2
Even number
/ 3
Sum of digits is a multiple of 3 (327 - 3 + 2 + 7) - 12
/ 4
If last two digits form a multiple of 4.
/ 5
If last digit is 0 or 5
/ 6
If rules of 2 and 3 are met
/ 9
If sum of digits is a multiple of 9
/ 10
If last digit is 0
Least common multiple
Smallest positive multiple shared by two or more integers.
How to find LCM
Reduce each element to its prime factors. LCM is product of highest counts of each separate prime
Greatest common factor
Largest factor shared between two or more integers
How to find GCF
Prime factor each integer. GCF is the product of the LOWEST counts of each prime common to both numbers
Multiples of N…
Occur every Nth integer. If you add or subtract a # that is not a multiple of N, result will not be a multiple of N
When checking to see if a number is prime…
You only need to check to see if the number is divisible by prime factors up to the approx sq. root of the number
Factoring trick
Factors come in pairs. To find factors, start at the bottom and work your way up to the middle
Unique factors does not mean
Prime factors
Unique factors trick (work #56)
1) Break number down to prime factors, expressing each as an exponent. (56 = 2^3 / 7^1)
2) Drop bases, take exponents and add one to each (4 and 2)
3 Multiply them (8)
Couples next to eachother on NL…
Have no factors in common.
