Given the Number 1,686,400, Calculate (Find) All the Factors (All the Divisors) of the Number 1,686,400 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,686,400

1. Carry out the prime factorization of the number 1,686,400:

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

1,686,400 = 27 × 52 × 17 × 31
1,686,400 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* 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 1,686,400

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
22 = 4
prime factor = 5
23 = 8
2 × 5 = 10
24 = 16
prime factor = 17
22 × 5 = 20
52 = 25
prime factor = 31
25 = 32
2 × 17 = 34
23 × 5 = 40
2 × 52 = 50
2 × 31 = 62
26 = 64
22 × 17 = 68
24 × 5 = 80
5 × 17 = 85
22 × 52 = 100
22 × 31 = 124
27 = 128
23 × 17 = 136
5 × 31 = 155
25 × 5 = 160
2 × 5 × 17 = 170
23 × 52 = 200
23 × 31 = 248
24 × 17 = 272
2 × 5 × 31 = 310
26 × 5 = 320
22 × 5 × 17 = 340
24 × 52 = 400
52 × 17 = 425
24 × 31 = 496
17 × 31 = 527
25 × 17 = 544
22 × 5 × 31 = 620
27 × 5 = 640
23 × 5 × 17 = 680
52 × 31 = 775
25 × 52 = 800
2 × 52 × 17 = 850
25 × 31 = 992
2 × 17 × 31 = 1,054
26 × 17 = 1,088
23 × 5 × 31 = 1,240
This list continues below...

... This list continues from above
24 × 5 × 17 = 1,360
2 × 52 × 31 = 1,550
26 × 52 = 1,600
22 × 52 × 17 = 1,700
26 × 31 = 1,984
22 × 17 × 31 = 2,108
27 × 17 = 2,176
24 × 5 × 31 = 2,480
5 × 17 × 31 = 2,635
25 × 5 × 17 = 2,720
22 × 52 × 31 = 3,100
27 × 52 = 3,200
23 × 52 × 17 = 3,400
27 × 31 = 3,968
23 × 17 × 31 = 4,216
25 × 5 × 31 = 4,960
2 × 5 × 17 × 31 = 5,270
26 × 5 × 17 = 5,440
23 × 52 × 31 = 6,200
24 × 52 × 17 = 6,800
24 × 17 × 31 = 8,432
26 × 5 × 31 = 9,920
22 × 5 × 17 × 31 = 10,540
27 × 5 × 17 = 10,880
24 × 52 × 31 = 12,400
52 × 17 × 31 = 13,175
25 × 52 × 17 = 13,600
25 × 17 × 31 = 16,864
27 × 5 × 31 = 19,840
23 × 5 × 17 × 31 = 21,080
25 × 52 × 31 = 24,800
2 × 52 × 17 × 31 = 26,350
26 × 52 × 17 = 27,200
26 × 17 × 31 = 33,728
24 × 5 × 17 × 31 = 42,160
26 × 52 × 31 = 49,600
22 × 52 × 17 × 31 = 52,700
27 × 52 × 17 = 54,400
27 × 17 × 31 = 67,456
25 × 5 × 17 × 31 = 84,320
27 × 52 × 31 = 99,200
23 × 52 × 17 × 31 = 105,400
26 × 5 × 17 × 31 = 168,640
24 × 52 × 17 × 31 = 210,800
27 × 5 × 17 × 31 = 337,280
25 × 52 × 17 × 31 = 421,600
26 × 52 × 17 × 31 = 843,200
27 × 52 × 17 × 31 = 1,686,400

The final answer:
(scroll down)

1,686,400 has 96 factors (divisors):
1; 2; 4; 5; 8; 10; 16; 17; 20; 25; 31; 32; 34; 40; 50; 62; 64; 68; 80; 85; 100; 124; 128; 136; 155; 160; 170; 200; 248; 272; 310; 320; 340; 400; 425; 496; 527; 544; 620; 640; 680; 775; 800; 850; 992; 1,054; 1,088; 1,240; 1,360; 1,550; 1,600; 1,700; 1,984; 2,108; 2,176; 2,480; 2,635; 2,720; 3,100; 3,200; 3,400; 3,968; 4,216; 4,960; 5,270; 5,440; 6,200; 6,800; 8,432; 9,920; 10,540; 10,880; 12,400; 13,175; 13,600; 16,864; 19,840; 21,080; 24,800; 26,350; 27,200; 33,728; 42,160; 49,600; 52,700; 54,400; 67,456; 84,320; 99,200; 105,400; 168,640; 210,800; 337,280; 421,600; 843,200 and 1,686,400
out of which 4 prime factors: 2; 5; 17 and 31
1,686,400 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.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 1,686,397?

» What are all the proper, improper and prime factors (divisors) of the number 1,686,414?


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

What are all the proper, improper and prime factors (all the divisors) of the number 2,099,326? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 1,686,400? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 14,469? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 1,524,978? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 259,200? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 54,125? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 4? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 94,918? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 24,066? How to calculate them? Apr 16 05:05 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 143,080? How to calculate them? Apr 16 05:05 UTC (GMT)
The list of all the calculated factors (divisors) of one or two numbers

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".