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Prime Numbers
A prime number is a number that has exactly two factors: 1 and itself. All whole numbers greater than 1 are either prime numbers or can be written as the product of prime numbers. There are an infinite number of prime numbers, but they occur less frequently among larger numbers. Prime numbers are important in cryptography and number theory.
30,833 Questions
What is a number between 1 and 1000 that has at least 7 prime numbers in its prime factorization?
27 = 128
What are the two primes that differ from 2?
There are infinitely many twin primes. One example is 5 and 7.
How can you find the number with the prime factorization of 2 2 times 32?
The number 32 cannot appear as a prime factor!
How do you check least common multiples by prime factorization?
You factor each of the two numbers (whose least common multiple your are looking for) down to all the prime numbers that multiply together to get those numbers.
Factoring Example: 36 = 6x6 = 2x3x2x3 = 2x2x3x3
Factoring Example: 7 = 7
Factoring Example: 15 = 3x5
Factoring Example 14 = 2x7
To get the least common multiple from the factors, you must look over all of the factors and take all of the UNIQUE ones with their highest multiples (like in 36 above, you have to take 2 twos and 2 threes) and multiply all of those together.
So... the least common multiple for 36 and 7 is 2x2x3x3x7 = 252
the least common multiple for 7 and 15 is 3x5x7 = 105
the least common multiple for 36 and 15 is 2x2x3x3x5 = 180
the least common multiple for 7 and 14 is 2x7 = 14
the least common multiple for 36 and 14 is 2x2x3x3x7= 252
Note: ALL of the factors of both numbers are in each answer, but no more than we need.
Keep in mind that LEAST common multiples are always equal to or GREATER than the larger of the two numbers. They are BIG numbers because they are multiples.
It is confusing when you learn GREATEST common factor, which is always LESS than or equal to the smaller of the two numbers. They are SMALL numbers because they are FACTORS.
Note: you can take least common multiples of more than two numbers:
Example: LCM of 14,15 & 36 is 2x2x3x3x5x7= 1260
If you write the prime factorizations of the numbers in power format, the lcm of the numbers is obtained by multiplying together the highest power of all the primes (across all the numbers).
eg lcm of 14, 15 & 36:
14 = 2 x 7
15 = 3 x 5
36 = 2^2 x 3^2
lcm = 2^2 x 3^2 x 5 x 7 = 1260
eg lcm 12, 14, 15:
12 = 2^2 x 3
14 = 2 x 7
15 = 3 x 5
lcm = 2^2 x 3 x 5 x 7 = 420
In this example, the highest power of 3 (which is 1) occurs in both 12 and 15, but it still only occurs once in the lcm.
Can you give some example of latin number?
Latin (Roman)............Decimal
V........... 5
X........... 10
L............ 50
C........... 100
