Recognised as Number

1,397,101

Positive
Odd
Prime
7 digits

1,397,101 is an odd 7-digit integer and a prime number. It has 2 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value1,397,101

Digit count7

Digit sum22

Digit product0zero, because one of the digits is zero

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation1,397,101

Distinct prime factors11,397,101

Number of divisors2

Sum of divisors σ(n)1,397,102

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)1,397,100integers below n that share no factor with it

Carmichael function λ(n)1,397,100the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 1,397,1012 in total

Arithmetic

Previous number1,397,100

Next number1,397,102

Double2,794,202

Half698,550.5

Square1,951,891,204,201

Cube2,726,989,153,280,421,301

Square root1,181.990270688≈irrational, shown to 9 decimal places

Cube root111.791624677≈

Negation-1,397,101

Reciprocal7.15767865 × 10^-7≈

Representations

Decimal1,397,101

Binary10101010100010110110121 bits

Octal5250555

Hexadecimal15516D

Base 36TY0D

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

In wordsone million, three hundred and ninety-seven thousand, one hundred and one

Ordinalone million, three hundred and ninety-seven thousand, one hundred and first

Scientific notation1.397101 × 10^6

Engineering notation1.397101 × 10^6

In other bases

Ternary2121222110111base 3; the most digit-efficient integer base after e: 13 digits

Quinary324201401base 5; one hand: 9 digits

Septenary14606116base 7: 8 digits

Nonary2558414base 9; each digit is two ternary digits: 7 digits

Duodecimal574611base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal8ecf1base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal6:28:5:1base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary10T0T00T110111digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary101010101011010111101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000101010101000101101101

Bit length21 bitsto write the magnitude

Set bits11the population count, or Hamming weight

Zero bits10within that length

Bit parityodd11 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes315 51 6d

Gray code111111111100111011011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000101010101000101101101

64-bit0000000000000000000000000000000000000000000101010101000101101101

One's complement11111111111010101010111010010010at 32 bits, every bit flipped

Bits reversed10110110100010101010100000000000at 32 bits

Rotated left by 100000000001010101010001011011010at 32 bits, wrapping

Shifted left by 11010101010001011011010= 2,794,202, no wrap

Shifted right by 110101010100010110110= 698,550, discarding the low bit

These bits as a double6.90259608 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,397,107+6

Previous prime1,397,087−14

Distance to nearest prime0, it is prime

Nearest square below1,394,761

Nearest square above1,397,124

Powers & multiples

1,397,101 to the power 21,951,891,204,201

1,397,101 to the power 32,726,989,153,280,421,301

1,397,101 to the power 43,809,879,273,037,229,880,048,401

1,397,101 to the power 55,322,786,142,239,586,902,645,501,085,501

First ten multiples1,397,101, 2,794,202, 4,191,303, 5,588,404, 6,985,505, 8,382,606, 9,779,707, 11,176,808, 12,573,909, 13,971,010

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 1

Divisible by 6No, remainder 1

Divisible by 7No, remainder 6

Divisible by 8No, remainder 5

Divisible by 9No, remainder 4

Divisible by 10No, remainder 1

Divisible by 11No, remainder 2

Divisible by 12No, remainder 1

Divisible by 100No, remainder 1

Collatz (3n + 1) trajectory

Steps to reach 175the total stopping time

Highest value reached5,035,2643× the starting value

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

First steps1,397,101 → 4,191,304 → 2,095,652 → 1,047,826 → 523,913 → 1,571,740 → 785,870 → 392,935 → 1,178,806 → 589,403 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage139,710,100%

1,397,101% as a decimal13,971.01

1,397,101% of 1001,397,101

1,397,101% of 1,00013,971,010

As a fraction of 1001,397,101/100

Read another way

As seconds16 days, 4 hours and 5 minutes

As bytes1.332 MiB

As a 24-bit colour#15516D

Keep nerding

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