Recognised as Number

1,337,616

Positive
Even
Composite
7 digits

1,337,616 is an even 7-digit integer and a composite number. It has 60 divisors and a digital root of 9.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,337,616

Digit count7

Digit sum27

Digit product2,268

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

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^4 × 3^2 × 7 × 1,327

Distinct prime factors42, 3, 7, 1,327

Number of divisors60

Sum of divisors σ(n)4,281,472

Aliquot sum2,943,856sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)381,888integers below n that share no factor with it

Carmichael function λ(n)2,652the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 381,888

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1,008, 1,327, 2,654, 3,981, 5,308, 7,962, 9,289, 10,616, 11,943, 15,924, 18,578, 21,232, 23,886, 27,867, 31,848, 37,156, 47,772, 55,734, 63,696, 74,312, 83,601, 95,544, 111,468, 148,624, 167,202, 191,088, 222,936, 334,404, 445,872, 668,808, 1,337,61660 in total

Arithmetic

Previous number1,337,615

Next number1,337,617

Double2,675,232

Half668,808

Square1,789,216,563,456

Cube2,393,284,702,743,760,896

Square root1,156.553500708≈irrational, shown to 9 decimal places

Cube root110.1819578≈

Negation-1,337,616

Reciprocal7.47598713 × 10^-7≈

Representations

Decimal1,337,616

Binary10100011010010001000021 bits

Octal5064420

Hexadecimal146910

Base 36SO40

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

In wordsone million, three hundred and thirty-seven thousand, six hundred and sixteen

Ordinalone million, three hundred and thirty-seven thousand, six hundred and sixteenth

Scientific notation1.337616 × 10^6

Engineering notation1.337616 × 10^6

In other bases

Ternary2111221212100base 3; the most digit-efficient integer base after e: 13 digits

Quinary320300431base 5; one hand: 9 digits

Septenary14240520base 7: 8 digits

Nonary2457770base 9; each digit is two ternary digits: 7 digits

Duodecimal546100base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal8740gbase 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal6:11:33:36base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary10TTT00T0TT100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary101011011100100010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000101000110100100010000

Bit length21 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits14within that length

Bit parityodd7 set bits, so odd; not the same as the number itself being even

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 44 trailing zeros

Power of twoNo

Bytes314 69 10

Gray code111100101110110011000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000101000110100100010000

64-bit0000000000000000000000000000000000000000000101000110100100010000

One's complement11111111111010111001011011101111at 32 bits, every bit flipped

Bits reversed00001000100101100010100000000000at 32 bits

Rotated left by 100000000001010001101001000100000at 32 bits, wrapping

Shifted left by 11010001101001000100000= 2,675,232, no wrap

Shifted right by 110100011010010001000= 668,808, discarding the low bit

These bits as a double6.60870113 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,337,617+1

Previous prime1,337,603−13

Distance to nearest prime1

Nearest square below1,336,336

Nearest square above1,338,649

Powers & multiples

1,337,616 to the power 21,789,216,563,456

1,337,616 to the power 32,393,284,702,743,760,896

1,337,616 to the power 43,201,295,910,945,298,474,663,936

1,337,616 to the power 54,282,104,631,215,006,364,486,075,416,576

First ten multiples1,337,616, 2,675,232, 4,012,848, 5,350,464, 6,688,080, 8,025,696, 9,363,312, 10,700,928, 12,038,544, 13,376,160

Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 1

Divisible by 6Yes

Divisible by 7Yes

Divisible by 8Yes

Divisible by 9Yes

Divisible by 10No, remainder 6

Divisible by 11No, remainder 5

Divisible by 12Yes

Divisible by 100No, remainder 16

Collatz (3n + 1) trajectory

Steps to reach 1111the total stopping time

Highest value reached1,337,616

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

First steps1,337,616 → 668,808 → 334,404 → 167,202 → 83,601 → 250,804 → 125,402 → 62,701 → 188,104 → 94,052 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage133,761,600%

1,337,616% as a decimal13,376.16

1,337,616% of 1001,337,616

1,337,616% of 1,00013,376,160

As a fraction of 1001,337,616/100

Read another way

As seconds15 days, 11 hours and 33 minutes

As bytes1.276 MiB

As a 24-bit colour#146910

Keep nerding

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