812,000: All the proper, improper and prime factors (divisors) of number

Factors of number 812,000

The fastest way to find all the factors (divisors) of 812,000: 1) Build its prime factorization & 2) Try out all the combinations of the prime factors that give different results

Note:

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



Integer prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


812,000 = 25 × 53 × 7 × 29;
812,000 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




How to find all the factors (divisors) of the number?

812,000 = 25 × 53 × 7 × 29


Get all the combinations (multiplications) of the prime factors of the number that give different results.


When combining the prime factors also consider their exponents.


Also add 1 to the list of factors (divisors). Any number is divisible by 1.


All the factors (divisors) are listed below, in ascending order.



Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
2 × 7 = 14
24 = 16
22 × 5 = 20
52 = 25
22 × 7 = 28
prime factor = 29
25 = 32
5 × 7 = 35
23 × 5 = 40
2 × 52 = 50
23 × 7 = 56
continued below...
... continued from above
2 × 29 = 58
2 × 5 × 7 = 70
24 × 5 = 80
22 × 52 = 100
24 × 7 = 112
22 × 29 = 116
53 = 125
22 × 5 × 7 = 140
5 × 29 = 145
25 × 5 = 160
52 × 7 = 175
23 × 52 = 200
7 × 29 = 203
25 × 7 = 224
23 × 29 = 232
2 × 53 = 250
23 × 5 × 7 = 280
2 × 5 × 29 = 290
2 × 52 × 7 = 350
24 × 52 = 400
2 × 7 × 29 = 406
24 × 29 = 464
22 × 53 = 500
24 × 5 × 7 = 560
22 × 5 × 29 = 580
22 × 52 × 7 = 700
52 × 29 = 725
25 × 52 = 800
22 × 7 × 29 = 812
53 × 7 = 875
25 × 29 = 928
23 × 53 = 1,000
5 × 7 × 29 = 1,015
25 × 5 × 7 = 1,120
23 × 5 × 29 = 1,160
23 × 52 × 7 = 1,400
2 × 52 × 29 = 1,450
23 × 7 × 29 = 1,624
2 × 53 × 7 = 1,750
24 × 53 = 2,000
2 × 5 × 7 × 29 = 2,030
24 × 5 × 29 = 2,320
24 × 52 × 7 = 2,800
22 × 52 × 29 = 2,900
24 × 7 × 29 = 3,248
22 × 53 × 7 = 3,500
53 × 29 = 3,625
25 × 53 = 4,000
22 × 5 × 7 × 29 = 4,060
25 × 5 × 29 = 4,640
52 × 7 × 29 = 5,075
25 × 52 × 7 = 5,600
23 × 52 × 29 = 5,800
25 × 7 × 29 = 6,496
23 × 53 × 7 = 7,000
2 × 53 × 29 = 7,250
23 × 5 × 7 × 29 = 8,120
2 × 52 × 7 × 29 = 10,150
24 × 52 × 29 = 11,600
24 × 53 × 7 = 14,000
22 × 53 × 29 = 14,500
24 × 5 × 7 × 29 = 16,240
22 × 52 × 7 × 29 = 20,300
25 × 52 × 29 = 23,200
53 × 7 × 29 = 25,375
25 × 53 × 7 = 28,000
23 × 53 × 29 = 29,000
25 × 5 × 7 × 29 = 32,480
23 × 52 × 7 × 29 = 40,600
2 × 53 × 7 × 29 = 50,750
24 × 53 × 29 = 58,000
24 × 52 × 7 × 29 = 81,200
22 × 53 × 7 × 29 = 101,500
25 × 53 × 29 = 116,000
25 × 52 × 7 × 29 = 162,400
23 × 53 × 7 × 29 = 203,000
24 × 53 × 7 × 29 = 406,000
25 × 53 × 7 × 29 = 812,000

Final answer:

812,000 has 96 factors:
1; 2; 4; 5; 7; 8; 10; 14; 16; 20; 25; 28; 29; 32; 35; 40; 50; 56; 58; 70; 80; 100; 112; 116; 125; 140; 145; 160; 175; 200; 203; 224; 232; 250; 280; 290; 350; 400; 406; 464; 500; 560; 580; 700; 725; 800; 812; 875; 928; 1,000; 1,015; 1,120; 1,160; 1,400; 1,450; 1,624; 1,750; 2,000; 2,030; 2,320; 2,800; 2,900; 3,248; 3,500; 3,625; 4,000; 4,060; 4,640; 5,075; 5,600; 5,800; 6,496; 7,000; 7,250; 8,120; 10,150; 11,600; 14,000; 14,500; 16,240; 20,300; 23,200; 25,375; 28,000; 29,000; 32,480; 40,600; 50,750; 58,000; 81,200; 101,500; 116,000; 162,400; 203,000; 406,000 and 812,000
out of which 4 prime factors: 2; 5; 7 and 29
812,000 (some consider that 1 too) is an improper factor (divisor), the others are proper factors (divisors).

The key to find the divisors of a number is to build its prime factorization.


Then determine all the different combinations (multiplications) of the prime factors, and their exponents, if any.



More operations of this kind:


Calculator: all the (common) factors (divisors) of numbers

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Tutoring: factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

If "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 12 = 22 × 3;
  • 48 = 24 × 3;
  • 360 = 23 × 32 × 5;
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples