The first twenty-six prime numbers are - ANSWER 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97,
101
Note: only positive numbers can be primes
all prime numbers above 3 are of the form - ANSWER 6n - 1 or 6n + 1
If is a positive integer greater than 1, then there is always a prime number - ANSWER P whth N<P<2N
If a number equals the sum of its proper divisors, it is said to be a perfect number. - ANSWER Example:
The proper divisors of 6 are 1, 2, and 3: 1+2+3=6, hence 6 is a perfect number.
If P is a prime number and P is a factor of AB then - ANSWER P is a factor of A or P is a factor of B.
Finding the Number of Factors of an Integer - ANSWER (p+1)(q+1)(r+1)....(z+1)
Finding the Sum of the Factors of an Integer - ANSWER (a^(p+1) - 1)*(b^(q+1) - 1)*(c^(r+1) - 1) / (a-1)(b-
1)(c-1)
Greatest Common Factor (Divisior) - GCF (GCD) - ANSWER The greatest common divisor (gcd), also
known as the greatest common factor (gcf), or
highest common factor (hcf), of two or more non-zero integers, is the largest positive
integer that divides the numbers without a remainder.
Every common divisor of a and b is a divisor of - ANSWER gcd(a, b).
gcd(a, b)*lcm(a, b) - ANSWER a*b
Lowest Common Multiple - LCM - ANSWER The lowest common multiple or lowest common multiple
(lcm) or smallest common
multiple of two integers a and b is the smallest positive integer that is a multiple both of a
and of b. Since it is a multiple, it can be divided by a and b without a remainder. If either
a or b is 0, so that there is no such positive integer, then lcm(a, b) is defined to be zero.
To find the LCM, you will need to do prime-factorization. Then multiply all the factors
(pick the highest power of the common factors).
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