Recognised as Number

49,007

Positive
Odd
Composite
5 digits

49,007 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value49,007

Digit count5

Digit sum20

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation7 × 7,001

Distinct prime factors27, 7,001

Number of divisors4

Sum of divisors σ(n)56,016

Aliquot sum7,009sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)42,000integers below n that share no factor with it

Carmichael function λ(n)21,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 42,000

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 7, 7,001, 49,0074 in total

Arithmetic

Previous number49,006

Next number49,008

Double98,014

Half24,503.5

Square2,401,686,049

Cube117,699,428,203,343

Square root221.375247035≈irrational, shown to 9 decimal places

Cube root36.594799544≈

Negation-49,007

Reciprocal0.0000204052≈

Representations

Decimal49,007

Binary101111110110111116 bits

Octal137557

HexadecimalBF6F

Base 3611TB

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

In wordsforty-nine thousand and seven

Ordinalforty-nine thousand and seventh

Scientific notation4.9007 × 10^4

Engineering notation49.007 × 10^3

In other bases

Ternary2111020002base 3; the most digit-efficient integer base after e: 10 digits

Quinary3032012base 5; one hand: 7 digits

Septenary262610base 7: 6 digits

Nonary74202base 9; each digit is two ternary digits: 5 digits

Duodecimal2443bbase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal62a7base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal13:36:47base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T1111T001Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11100000010110011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1011111101101111

Bit length16 bitsto write the magnitude

Set bits13the population count, or Hamming weight

Zero bits3within that length

Bit parityodd13 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes2bf 6f

Gray code1110000011011000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1011111101101111

32-bit00000000000000001011111101101111

64-bit0000000000000000000000000000000000000000000000001011111101101111

One's complement0100000010010000at 16 bits, every bit flipped

Bits reversed1111011011111101at 16 bits

Rotated left by 10111111011011111at 16 bits, wrapping

Shifted left by 110111111011011110= 98,014, no wrap

Shifted right by 1101111110110111= 24,503, discarding the low bit

These bits as a double2.42126751 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime49,009+2

Previous prime49,003−4

Distance to nearest prime2

Nearest square below48,841

Nearest square above49,284

Powers & multiples

49,007 to the power 22,401,686,049

49,007 to the power 3117,699,428,203,343

49,007 to the power 45,768,095,877,961,230,401

49,007 to the power 5282,677,074,691,246,018,261,807

First ten multiples49,007, 98,014, 147,021, 196,028, 245,035, 294,042, 343,049, 392,056, 441,063, 490,070

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 3

Divisible by 5No, remainder 2

Divisible by 6No, remainder 5

Divisible by 7Yes

Divisible by 8No, remainder 7

Divisible by 9No, remainder 2

Divisible by 10No, remainder 7

Divisible by 11No, remainder 2

Divisible by 12No, remainder 11

Divisible by 100No, remainder 7

Collatz (3n + 1) trajectory

Steps to reach 1171the total stopping time

Highest value reached558,23211× the starting value

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

First steps49,007 → 147,022 → 73,511 → 220,534 → 110,267 → 330,802 → 165,401 → 496,204 → 248,102 → 124,051 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,900,700%

49,007% as a decimal490.07

49,007% of 10049,007

49,007% of 1,000490,070

As a fraction of 10049,007/100

Read another way

As seconds13 hours, 36 minutes and 47 seconds

As bytes47.858 KiB

As a 24-bit colour#00BF6F

Keep nerding

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