Given the Number 2,410,800 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 2,410,800

1. Carry out the prime factorization of the number 2,410,800:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


2,410,800 = 24 × 3 × 52 × 72 × 41
2,410,800 is not a prime number but a composite one.


* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 2,410,800

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.


Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


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

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
24 = 16
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
22 × 7 = 28
2 × 3 × 5 = 30
5 × 7 = 35
23 × 5 = 40
prime factor = 41
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
2 × 52 = 50
23 × 7 = 56
22 × 3 × 5 = 60
2 × 5 × 7 = 70
3 × 52 = 75
24 × 5 = 80
2 × 41 = 82
22 × 3 × 7 = 84
2 × 72 = 98
22 × 52 = 100
3 × 5 × 7 = 105
24 × 7 = 112
23 × 3 × 5 = 120
3 × 41 = 123
22 × 5 × 7 = 140
3 × 72 = 147
2 × 3 × 52 = 150
22 × 41 = 164
23 × 3 × 7 = 168
52 × 7 = 175
22 × 72 = 196
23 × 52 = 200
5 × 41 = 205
2 × 3 × 5 × 7 = 210
24 × 3 × 5 = 240
5 × 72 = 245
2 × 3 × 41 = 246
23 × 5 × 7 = 280
7 × 41 = 287
2 × 3 × 72 = 294
22 × 3 × 52 = 300
23 × 41 = 328
24 × 3 × 7 = 336
2 × 52 × 7 = 350
23 × 72 = 392
24 × 52 = 400
2 × 5 × 41 = 410
22 × 3 × 5 × 7 = 420
2 × 5 × 72 = 490
22 × 3 × 41 = 492
3 × 52 × 7 = 525
24 × 5 × 7 = 560
2 × 7 × 41 = 574
22 × 3 × 72 = 588
23 × 3 × 52 = 600
3 × 5 × 41 = 615
24 × 41 = 656
22 × 52 × 7 = 700
3 × 5 × 72 = 735
24 × 72 = 784
22 × 5 × 41 = 820
23 × 3 × 5 × 7 = 840
3 × 7 × 41 = 861
22 × 5 × 72 = 980
23 × 3 × 41 = 984
52 × 41 = 1,025
2 × 3 × 52 × 7 = 1,050
22 × 7 × 41 = 1,148
23 × 3 × 72 = 1,176
24 × 3 × 52 = 1,200
52 × 72 = 1,225
2 × 3 × 5 × 41 = 1,230
23 × 52 × 7 = 1,400
5 × 7 × 41 = 1,435
2 × 3 × 5 × 72 = 1,470
This list continues below...

... This list continues from above
23 × 5 × 41 = 1,640
24 × 3 × 5 × 7 = 1,680
2 × 3 × 7 × 41 = 1,722
23 × 5 × 72 = 1,960
24 × 3 × 41 = 1,968
72 × 41 = 2,009
2 × 52 × 41 = 2,050
22 × 3 × 52 × 7 = 2,100
23 × 7 × 41 = 2,296
24 × 3 × 72 = 2,352
2 × 52 × 72 = 2,450
22 × 3 × 5 × 41 = 2,460
24 × 52 × 7 = 2,800
2 × 5 × 7 × 41 = 2,870
22 × 3 × 5 × 72 = 2,940
3 × 52 × 41 = 3,075
24 × 5 × 41 = 3,280
22 × 3 × 7 × 41 = 3,444
3 × 52 × 72 = 3,675
24 × 5 × 72 = 3,920
2 × 72 × 41 = 4,018
22 × 52 × 41 = 4,100
23 × 3 × 52 × 7 = 4,200
3 × 5 × 7 × 41 = 4,305
24 × 7 × 41 = 4,592
22 × 52 × 72 = 4,900
23 × 3 × 5 × 41 = 4,920
22 × 5 × 7 × 41 = 5,740
23 × 3 × 5 × 72 = 5,880
3 × 72 × 41 = 6,027
2 × 3 × 52 × 41 = 6,150
23 × 3 × 7 × 41 = 6,888
52 × 7 × 41 = 7,175
2 × 3 × 52 × 72 = 7,350
22 × 72 × 41 = 8,036
23 × 52 × 41 = 8,200
24 × 3 × 52 × 7 = 8,400
2 × 3 × 5 × 7 × 41 = 8,610
23 × 52 × 72 = 9,800
24 × 3 × 5 × 41 = 9,840
5 × 72 × 41 = 10,045
23 × 5 × 7 × 41 = 11,480
24 × 3 × 5 × 72 = 11,760
2 × 3 × 72 × 41 = 12,054
22 × 3 × 52 × 41 = 12,300
24 × 3 × 7 × 41 = 13,776
2 × 52 × 7 × 41 = 14,350
22 × 3 × 52 × 72 = 14,700
23 × 72 × 41 = 16,072
24 × 52 × 41 = 16,400
22 × 3 × 5 × 7 × 41 = 17,220
24 × 52 × 72 = 19,600
2 × 5 × 72 × 41 = 20,090
3 × 52 × 7 × 41 = 21,525
24 × 5 × 7 × 41 = 22,960
22 × 3 × 72 × 41 = 24,108
23 × 3 × 52 × 41 = 24,600
22 × 52 × 7 × 41 = 28,700
23 × 3 × 52 × 72 = 29,400
3 × 5 × 72 × 41 = 30,135
24 × 72 × 41 = 32,144
23 × 3 × 5 × 7 × 41 = 34,440
22 × 5 × 72 × 41 = 40,180
2 × 3 × 52 × 7 × 41 = 43,050
23 × 3 × 72 × 41 = 48,216
24 × 3 × 52 × 41 = 49,200
52 × 72 × 41 = 50,225
23 × 52 × 7 × 41 = 57,400
24 × 3 × 52 × 72 = 58,800
2 × 3 × 5 × 72 × 41 = 60,270
24 × 3 × 5 × 7 × 41 = 68,880
23 × 5 × 72 × 41 = 80,360
22 × 3 × 52 × 7 × 41 = 86,100
24 × 3 × 72 × 41 = 96,432
2 × 52 × 72 × 41 = 100,450
24 × 52 × 7 × 41 = 114,800
22 × 3 × 5 × 72 × 41 = 120,540
3 × 52 × 72 × 41 = 150,675
24 × 5 × 72 × 41 = 160,720
23 × 3 × 52 × 7 × 41 = 172,200
22 × 52 × 72 × 41 = 200,900
23 × 3 × 5 × 72 × 41 = 241,080
2 × 3 × 52 × 72 × 41 = 301,350
24 × 3 × 52 × 7 × 41 = 344,400
23 × 52 × 72 × 41 = 401,800
24 × 3 × 5 × 72 × 41 = 482,160
22 × 3 × 52 × 72 × 41 = 602,700
24 × 52 × 72 × 41 = 803,600
23 × 3 × 52 × 72 × 41 = 1,205,400
24 × 3 × 52 × 72 × 41 = 2,410,800

The final answer:
(scroll down)

2,410,800 has 180 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 14; 15; 16; 20; 21; 24; 25; 28; 30; 35; 40; 41; 42; 48; 49; 50; 56; 60; 70; 75; 80; 82; 84; 98; 100; 105; 112; 120; 123; 140; 147; 150; 164; 168; 175; 196; 200; 205; 210; 240; 245; 246; 280; 287; 294; 300; 328; 336; 350; 392; 400; 410; 420; 490; 492; 525; 560; 574; 588; 600; 615; 656; 700; 735; 784; 820; 840; 861; 980; 984; 1,025; 1,050; 1,148; 1,176; 1,200; 1,225; 1,230; 1,400; 1,435; 1,470; 1,640; 1,680; 1,722; 1,960; 1,968; 2,009; 2,050; 2,100; 2,296; 2,352; 2,450; 2,460; 2,800; 2,870; 2,940; 3,075; 3,280; 3,444; 3,675; 3,920; 4,018; 4,100; 4,200; 4,305; 4,592; 4,900; 4,920; 5,740; 5,880; 6,027; 6,150; 6,888; 7,175; 7,350; 8,036; 8,200; 8,400; 8,610; 9,800; 9,840; 10,045; 11,480; 11,760; 12,054; 12,300; 13,776; 14,350; 14,700; 16,072; 16,400; 17,220; 19,600; 20,090; 21,525; 22,960; 24,108; 24,600; 28,700; 29,400; 30,135; 32,144; 34,440; 40,180; 43,050; 48,216; 49,200; 50,225; 57,400; 58,800; 60,270; 68,880; 80,360; 86,100; 96,432; 100,450; 114,800; 120,540; 150,675; 160,720; 172,200; 200,900; 241,080; 301,350; 344,400; 401,800; 482,160; 602,700; 803,600; 1,205,400 and 2,410,800
out of which 5 prime factors: 2; 3; 5; 7 and 41
2,410,800 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.


Then multiply the prime factors and their exponents, if any, in all their different combinations.


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 the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • 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 the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 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, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • 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).
  • Factors of the GCF
  • 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".