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Examples for

Step-by-Step Discrete Mathematics

Number Values

See how to determine the absolute value of a number:

absolute value of -19
abs(46)
|-288|

Fractions, Ratios & Percents

Convert a fraction to a mixed number step by step:

87/5 as a mixed number
convert 61/4 to a mixed number

Get step-by-step solutions for converting between percents and fractions:

64% as a fraction
what is 12.35% as a fraction?

Learn how to make conversions between percents and decimals:

40% as a decimal number
63.8% as a decimal

Divisors

See how to compute all the divisors of a number step by step:

divisors of 92
divisors of 45
divisors 19

Learn how to find the total number of divisors of a given number:

number of divisors of 20

Follow the steps to find the sum of the divisors:

sum of divisors of 30

See step-by-step solutions for the divisor function:

divisor sigma(0, 10)
divisor sigma(1, 8)
divisor sigma(2, 15)

Learn how to check if a number is square free:

Is 210 square-free?

Base Conversions

Get the steps for converting numbers to binary:

convert 12345 to binary
876 to base 2

Learn how to convert numbers to hexadecimal:

convert 7652 to hexadecimal
76231528 to base 16

Convert between integer bases from binary to base 36:

convert 33ab3653 base 12 to base 10
0xa4fb in binary
convert cat from base 36 to base 35

See the steps to add or subtract integers in bases 2 through 9:

102 base 3 + 21 base 3
5^^123 - 4^^123
12_3 + 45_6 + 78_9

Divisibility

See the steps to determine divisibility:

is 282 divisible by 47?
14 divisible by 5
is 126 divisible by 7?
is 4878 divisible by 9?

Prime Numbers

Find step-by-step solutions for testing if a number is prime or composite:

is 73 prime?
primality 290
is 543 prime or composite?

GCD & LCM

See the steps for finding a greatest common divisor:

gcd(56, 24)
greatest common divisor of {12, 45, 72}
88 and 154 greatest common factor

Find a least common multiple:

lcm(90, 342)
least common multiple {12, 56, 27}

See step-by-step solutions for determining if two integers are coprime:

are 12 and 21 coprime?
are 14 and 27 coprime?

Count the positive integers coprime to and less than a given number:

Euler phi 36
totient 13

Arithmetic Functions

Learn how to evaluate arithmetic functions step by step:

Moebius mu of 9
Mangoldt lambda of 27
what is PrimeNu[48]
what is PrimeOmega[48]
what is Liouville lambda of 24

RELATED EXAMPLES

  • Base Conversions
  • Discrete Mathematics
  • Number Theory

    • Prime Factorization

    Perform prime factorization one step at a time:

    factor 72
    5040 factorization
    prime factors 47
    prime factorization of 56

    Exponents & Roots

    See the steps for computing the value of a number raised to a power:

    4^3
    12^5

    Multiply numbers with exponents step by step:

    3^2 * 3^5
    4^3 * 8^2

    Divide numbers with exponents:

    (7^9)/(7^4)
    3^4 / 9^3

    Get the steps for simplifying expressions with radicals:

    square root of 25
    sqrt(81)
    simplify sqrt(45)
    simplify 24^(1/2)
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