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Can you express every odd prime number as the difference of two squares?
Every odd number greater than one is the difference of two squares. This includes all the odd prime numbers. To find the two numbers whose difference of squares equals a particular odd number, divide the odd number by 2. The two numbers are the integers immediately below and above that dividend. For example, 17 is the difference of two squares. Divide 17 by 2 and get 8.5. The two numbers are 8 and 9. 92 - 82 = 81 - 64 = 17.
Can you express every odd prime number as the difference of two square numbers?
All odd numbers are in the form of (2n + 1) form some integer n. (2n + 1) can be expanded into (n+1)^2 + n^2, which is the difference of two squares.
How do you express a number as the product of powers of its prime factors?
You factor the number into prime factors, dividing each prime out.
Express 7 as a product of prime factor?
None. 7 is a prime number.
What are 2 prime numbers less than 20 whose difference is a prime number?
2 and 5 the difference is 3 which is a prime number
Can you express every odd prime number as the difference of two squares?
Every odd number greater than one is the difference of two squares. This includes all the odd prime numbers. To find the two numbers whose difference of squares equals a particular odd number, divide the odd number by 2. The two numbers are the integers immediately below and above that dividend. For example, 17 is the difference of two squares. Divide 17 by 2 and get 8.5. The two numbers are 8 and 9. 92 - 82 = 81 - 64 = 17.
Does the difference of two squares number always factorable?
No. If the two numbers are consecutive then the difference of their squares need not be factorisable. For example, 4^3 - 3^3 = 16 - 9 = 7, which is a prime. If the smaller number is a then this simply requires that 2a+1 is a prime.
Can you express every odd prime number as the difference of two square numbers?
All odd numbers are in the form of (2n + 1) form some integer n. (2n + 1) can be expanded into (n+1)^2 + n^2, which is the difference of two squares.
Will you get the same number of factors if you multiply a prime number and itself?
Prime numbers have two factors. Prime squares have three factors. Square numbers have an odd number of factors but that number varies.
What number has exactly 3 factors?
Prime squares
Will you get the same number of factors if you multiply a prime number by itself?
All prime squares have three factors.
Can a number be both prime and square?
No. A prime number is divisible only by itself and 1. Squares have other factors.
Is the difference of two prime numbers a prime number?
Not necessarily. 71 is a prime number, 7 is a prime number, and 71-7= 64, which is NOT a prime number. In most cases, the difference of two prime numbers will not be a prime number. All prime numbers greater than 2 will be odd numbers. The difference between two odd numbers will be an even number. Unless that even number is 2, it is not a prime number. Here are some additional examples: 19, 13: difference 6, not prime 23, 7: difference 16, not prime 53, 31: difference 22, not prime 61, 59: difference 2, prime 113, 109: difference 4, not prime 293, 283: difference 10, not prime 331, 101: difference 230, not prime
What is a number with only 3 factors called?
Any square of a prime number. For example, 5*5 = 25 has the factors 1, 5, 25. If you square any other prime number, call it "p", the factors of the result are 1, p, p square.
How many numbers has three factors?
There are an infinite number of prime squares.
What number only have three factors?
squares of prime numbers
Identify a number on the table that has exactly 3 factors?
Prime squares
