Recognised as Number

13,472

Positive
Even
Composite
5 digits

13,472 is an even 5-digit integer and a composite number. It has 12 divisors and a digital root of 8.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value13,472

Digit count5

Digit sum17

Digit product168

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberYessquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 421

Distinct prime factors22, 421

Number of divisors12

Sum of divisors σ(n)26,586

Aliquot sum13,114sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)6,720integers below n that share no factor with it

Carmichael function λ(n)840the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 6,720

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 16, 32, 421, 842, 1,684, 3,368, 6,736, 13,47212 in total

Arithmetic

Previous number13,471

Next number13,473

Double26,944

Half6,736

Square181,494,784

Cube2,445,097,730,048

Square root116.068945028≈irrational, shown to 9 decimal places

Cube root23.794542448≈

Negation-13,472

Reciprocal0.000074228≈

Representations

Decimal13,472

Binary1101001010000014 bits

Octal32240

Hexadecimal34A0

Base 36AE8

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

In wordsthirteen thousand, four hundred and seventy-two

Ordinalthirteen thousand, four hundred and seventy-second

Scientific notation1.3472 × 10^4

Engineering notation13.472 × 10^3

In other bases

Ternary200110222base 3; the most digit-efficient integer base after e: 9 digits

Quinary412342base 5; one hand: 6 digits

Septenary54164base 7: 5 digits

Nonary20428base 9; each digit is two ternary digits: 5 digits

Duodecimal7968base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1ddcbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:44:32base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0011100Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary111010111100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010010100000

Bit length14 bitsto write the magnitude

Set bits5the population count, or Hamming weight

Zero bits9within that length

Bit parityodd5 set bits, so odd; not the same as the number itself being even

Highest set bitbit 13worth 8,192

Lowest set bitbit 55 trailing zeros

Power of twoNo

Bytes234 a0

Gray code10111011110000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010010100000

32-bit00000000000000000011010010100000

64-bit0000000000000000000000000000000000000000000000000011010010100000

One's complement1100101101011111at 16 bits, every bit flipped

Bits reversed0000010100101100at 16 bits

Rotated left by 10110100101000000at 16 bits, wrapping

Shifted left by 1110100101000000= 26,944, no wrap

Shifted right by 11101001010000= 6,736, discarding the low bit

These bits as a double6.65605238 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,477+5

Previous prime13,469−3

Distance to nearest prime3

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,472 to the power 2181,494,784

13,472 to the power 32,445,097,730,048

13,472 to the power 432,940,356,619,206,656

13,472 to the power 5443,772,484,373,952,069,632

First ten multiples13,472, 26,944, 40,416, 53,888, 67,360, 80,832, 94,304, 107,776, 121,248, 134,720

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 5No, remainder 2

Divisible by 6No, remainder 2

Divisible by 7No, remainder 4

Divisible by 8Yes

Divisible by 9No, remainder 8

Divisible by 10No, remainder 2

Divisible by 11No, remainder 8

Divisible by 12No, remainder 8

Divisible by 100No, remainder 72

Collatz (3n + 1) trajectory

Steps to reach 145the total stopping time

Highest value reached13,472

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

First steps13,472 → 6,736 → 3,368 → 1,684 → 842 → 421 → 1,264 → 632 → 316 → 158 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,347,200%

13,472% as a decimal134.72

13,472% of 10013,472

13,472% of 1,000134,720

As a fraction of 10013,472/100

Read another way

As seconds3 hours, 44 minutes and 32 seconds

As bytes13.156 KiB

As a 24-bit colour#0034A0

Keep nerding

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