Number

13,400

Positive
Even
Composite
5 digits

13,400 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 8.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value13,400

Digit count5

Digit sum8

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^3 × 5^2 × 67

Distinct prime factors32, 5, 67

Number of divisors24

Sum of divisors σ(n)31,620

Aliquot sum18,220sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)5,280integers below n that share no factor with it

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 134, 200, 268, 335, 536, 670, 1,340, 1,675, 2,680, 3,350, 6,700, 13,40024 in total

Arithmetic

Previous number13,399

Next number13,401

Double26,800

Half6,700

Square179,560,000

Cube2,406,104,000,000

Square root115.758369028≈irrational, shown to 9 decimal places

Cube root23.752077381≈

Negation-13,400

Reciprocal0.0000746269≈

Representations

Decimal13,400

Binary1101000101100014 bits

Octal32130

Hexadecimal3458

Base 36AC8

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsthirteen thousand, four hundred

Ordinalthirteen thousand, four hundredth

Scientific notation1.34 × 10^4

Engineering notation13.4 × 10^3

Nearest landmarks

Next prime13,411+11

Previous prime13,399−1

Distance to nearest prime1

Nearest square below13,225

Nearest square above13,456

Powers & multiples

13,400 to the power 2179,560,000

13,400 to the power 32,406,104,000,000

13,400 to the power 432,241,793,600,000,000

13,400 to the power 5432,040,034,240,000,000,000

First ten multiples13,400, 26,800, 40,200, 53,600, 67,000, 80,400, 93,800, 107,200, 120,600, 134,000

Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6No, remainder 2

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 8

Divisible by 10Yes

Divisible by 11No, remainder 2

Divisible by 12No, remainder 8

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 1138the total stopping time

Highest value reached13,400

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps13,400 → 6,700 → 3,350 → 1,675 → 5,026 → 2,513 → 7,540 → 3,770 → 1,885 → 5,656 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,340,000%

13,400% as a decimal134

13,400% of 10013,400

13,400% of 1,000134,000

As a fraction of 10013,400/100

Read another way

As seconds3 hours, 43 minutes and 20 seconds

As bytes13.086 KiB

As a 24-bit colour#003458

Keep nerding

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