3-Number Theory-Factoring

factoring numbers

Smaller numbers, excluding one, can divide into whole numbers with no remainders {factoring, numbers} {factor, number} {associate, number}. Most whole numbers {composite number} have factors.

Theories {theory of ideal numbers} {ideal numbers theory} can find unique factorization into primes.

divisible by 11

If integer is divisible by 11, sum of digits with alternating sign is 0. For example, 121 (1 - 2 + 1 = 0) is divisible by 11, but 1234 (1 - 2 + 3 - 4 = -2) is not divisible by 11.

divisible by 3

If integer is divisible by 3, sum of digits is divisible by 3. For example, 24 (2 + 4 = 6) is divisible by 3, but 38 (3 + 8 = 11) is not divisible by 3.

divisible by 5

If integer is divisible by 5, last digit must be 0 or 5. For example, 25 and 30 are divisible by 5.

fundamental theorem of arithmetic

All natural numbers, except the number one, factor into primes in only one way {fundamental theorem of arithmetic}.

greatest common factor

Two numbers have largest factor in common {greatest common factor, number}. First divide smaller number into larger. Then divide remainder into smaller. Then divide new remainder into first remainder. Continue until remainder is zero. Greatest common factor is remainder obtained just before remainder is zero. Greatest common factor is product of shared prime factors.

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3-Number Theory

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Date Modified: 2022.0225