# Mathematical Operations With Prime Numbers

## Latest factored numbers (latest prime factorizations)

 81,152,427 = 3 × 433 × 62473 Dec 05 22:46 UTC (GMT) 5,153,294,382 = 2 × 3 × 858882397 Dec 05 22:46 UTC (GMT) 43,748 = 22 × 10937 Dec 05 22:46 UTC (GMT) see more... integer numbers factored, broken down to prime factors

## The latest calculated greatest (highest) common factors (divisors), gcf (hcf, gcd)

 gcf, hcf, gcd (24,000; 106,000) = 2,000 = 24 × 53 Dec 05 22:46 UTC (GMT) gcf, hcf, gcd (9,498; 231) = 3 Dec 05 22:46 UTC (GMT) gcf, hcf, gcd (473; 645) = 43 Dec 05 22:46 UTC (GMT) gcf, hcf, gcd, see more...

## The latest calculated values of the "least common multiple", LCM

 lcm (48; 152) = 912 = 24 × 3 × 19 Dec 05 22:46 UTC (GMT) lcm (588; 336) = 2,352 = 24 × 3 × 72 Dec 05 22:46 UTC (GMT) lcm (1,030; 270) = 27,810 = 2 × 33 × 5 × 103 Dec 05 22:46 UTC (GMT) least common multiple, see more...

## Latest fractions reduced (simplified) to the lowest terms

 98/648 = (98 ÷ 2)/(648 ÷ 2) = 49/324 Dec 05 22:46 UTC (GMT) 8/4,317 already reduced (simplified) to lowest terms Dec 05 22:46 UTC (GMT) 204/15 = (204 ÷ 3)/(15 ÷ 3) = 68/5; 68 > 5 => improper fraction Rewrite: 68 ÷ 5 = 13 and remainder = 3 => 68/5 = (13 × 5 + 3)/5 = 13 + 3/5 = = 13 3/5, mixed number (mixed fraction) Dec 05 22:46 UTC (GMT) reduced fractions, see more...

## The latest numbers that were checked to see whether they are divisible or not

 Number 1,274 is not divisible by 78. Number 1,274 does not have (all) the prime factors of the number 78. Dec 05 22:46 UTC (GMT) Number 67 is not divisible by 5. Number 67 does not have (all) the prime factors of the number 5. Dec 05 22:46 UTC (GMT) Number 576 is divisible by 4. Number 576 has all the prime factors of the number 4. Dec 05 22:45 UTC (GMT) integer numbers divisibility, see more...

## Latest calculated factors (divisors)

 common factors (divisors) (36; 6,837) = ? Dec 05 22:46 UTC (GMT) common factors (divisors) (3; 50) = ? Dec 05 22:46 UTC (GMT) common factors (divisors) (3; 50) = ? Dec 05 22:46 UTC (GMT) common factors (divisors), see more...

## Coprime numbers or not (relatively prime, prime to each other or not)? Latest operations

 coprime numbers (relatively prime) (1,894; 448)? Dec 05 22:45 UTC (GMT) coprime numbers (relatively prime) (1,000; 3,457)? Dec 05 22:45 UTC (GMT) coprime numbers (relatively prime) (16; 4,094)? Dec 05 22:45 UTC (GMT) coprime numbers (relatively prime), see more...

## Latest numbers tested on parity: even or odd?

 parity (49,787,137) = odd Dec 05 22:46 UTC (GMT) parity (390,420,113) = odd Dec 05 22:46 UTC (GMT) parity (21,400) = even Dec 05 22:45 UTC (GMT) parity, see more...

## Prime numbers definition. Composite numbers

#### A composite number is a positive integer that has at least one positive divisor other than 1 and the number itself. A composite number is also any positive integer larger than 1 that is not a prime number.

• 2 is divisible only by 2 and 1, so 2 is a prime number
• 3 is divisible only by 3 and 1, so 3 is a prime number
• 5 is divisible only by 5 and 1, so 5 is a prime number
• 13 is divisible only by 13 and 1, so 13 is a prime number

#### 1 is not considered prime, so the first prime number is 2 (prime numbers list is starting with the number 2)

##### The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers in a way that is unique, except for the order of the prime factors. Prime numbers are thus the basic building blocks of all numbers. If 1 were admitted as a prime, number 15 for example could be factored as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations of 15 (prime factorization into prime factors), so the statement of the theorem would have to be modified.
• 4 is divisible by 4, 2 and 1, so 4 is not a prime number, it's a composite number; 4 = 22
• 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime number, it's a composite number; 6 = 2 × 3
• 8 is divisible by 8, 4, 2 and 1, so 8 is not a prime number, it's a composite number; 8 = 23
• 9 is divisible by 9, 3, and 1, so 9 is not a prime number, it's a composite number; 9 = 32

Examples of prime numbers, up to 100: 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