Math Question: Can you find two numbers whose product is 72 and whose sum is equal to the square root of their difference plus the square root of their average?

Sure! Let's solve the problem step by step. Let the two numbers be x and y. The product of two numbers: xy = 72. Their sum: x + y = √(x - y) + √((x + y)/2). To solve this equation, let's assume x > y. Squaring both sides, we get: (x + y)² = (x - y) + 2√(x² - xy) + (x + y)/2. Expanding and simplifying, we have: x² + 2xy + y² = x - y + 2√(x² - 72) + (x + y)/2. Rearranging: (x + y)/2 + y² - x² = x - y + 2√(x² - 72). Simplifying further: 2y² + 2xy - 2x² = 2√(x² - 72). Dividing both sides by 2: y² + xy - x² = √(x² - 72). Now, let's substitute xy = 72: y² + 72/x - x² = √(x² - 72). This is a quadratic equation in terms of y. Solving it will give us the possible values of x and y. The positive solutions to this equation are x = 8 and y = 9. Therefore, the numbers whose product is 72 and whose sum is equal to the given expression are 8 and 9.

Math question: What is the product of the prime factors of 72?

To find the prime factors of 72, we first divide it by the smallest prime number, 2. The result is 36. By dividing again with 2, we get 18. Continuing this process, we divide by 2 again to get 9. Now, 9 is divisible by 3. Thus, the prime factors of 72 are 2, 2, 2, and 3. The product of these prime factors is calculated as 2 x 2 x 2 x 3 = 24. Therefore, the product of the prime factors of 72 is 24.

Math Question: What is the absolute difference between the sum of the positive odd factors and the sum of the positive even factors of the number 72?

To find the positive odd factors of 72, we need to list the numbers that divide 72 without leaving a remainder, and which are odd. These factors are 1, 3, 9, 27, and 72 itself. Adding these odd factors gives 1 + 3 + 9 + 27 + 72 = 112. To determine the positive even factors of 72, we list the numbers that divide 72 without leaving a remainder, and which are even. These factors are 2, 4, 6, 8, 12, 18, 24, 36. Adding these even factors gives 2 + 4 + 6 + 8 + 12 + 18 + 24 + 36 = 110. The absolute difference between the sum of the positive odd factors (112) and the sum of the positive even factors (110) of the number 72 is |112 - 110| = 2. Therefore, the answer is 2.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

72 (number)

72 is an even 2-digits composite number following 71 and preceding 73. In scientific notation, it is written as 7.2 × 10^1. The sum of its digits is 9. It has a total of 5 prime factors and 12 positive divisors. There are 24 positive integers (up to 72) that are relatively prime to 72.

Interesting facts

72 has 12 divisors, whose sum is 195
The reverse of 72 is 27
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 2
Sum of Digits 9
Digital Root 9

Name

Name	seventy-two

Notation

Scientific notation	7.2 × 10^1
Engineering notation	7.2 × 10^0

Prime Factorization of 72

Prime Factorization 2 × 2 × 2 × 3 × 3

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	5	Total number of prime factors
rad	Radical	6	Product of the distinct prime numbers

The prime factorization of 72 is 2 × 2 × 2 × 3 × 3. Since it has a total of 5 prime factors.

Most popular turbo-numbers

6, 10, 30, 84, 239, 654, 5680, 224, 64075, 91563, 140673, 42916, 7716495, 6074444, 97500535, 21734792, 353911184, 706372143, 2919286250, 8959324805

Basic calculations (n = 72)

Multiplication

n×y

n×2	144
n×3	216
n×4	288
n×5	360

Division

n÷y

n÷2	36
n÷3	24
n÷3	18
n÷5	14.4

Exponentiation

n^y

n²	5184
n³	373248
n⁴	26873856
n⁵	1934917632

Nth Root

^y√n

²√n	8.4852813742386
³√n	4.1601676461038
⁴√n	2.9129506302439
⁵√n	2.3521580450493

Divisors of 72

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

12 divisors

τ	Total Divisors	12	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-71	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.083333333333333	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	12	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 72 can be divided by 12 positive divisors. The sum of these divisors (counting 72) is 1, the average is 0.083333333333333.

Base conversion 72

Base	System	Value
2	Binary	1001000
3	Ternary	2200
4	Quaternary	1020
5	Quinary	242
6	Senary	200
8	Octal	110
10	Decimal	72
12	Duodecimal	60
16	Hexadecimal	48
20	Vigesimal	3c
36	Base36	20

Cryptographic Hash Functions

md5	32bb90e8976aab5298d5da10fe66f21d
sha1	c097638f92de80ba8d6c696b26e6e601a5f61eb7
sha256	8722616204217eddb39e7df969e0698aed8e599ba62ed2de1ce49b03ade0fede
sha512	8bd4964ded25d2608bbfd709784f9ca9893b6e3e51ec556d7c368c561a2c4f4135266ec7bb6fdeb3651213ea2a8eaf2ef3711b8a51f86c3816c821a62d2694ea
ripemd-160	459ee276403df3ef718024b910bdf40eee41cc31

72 as geometric shapes

Circle

Radius = n

Diameter	144
Circumference	452.38934211693
Area	16286.016316209

Sphere

Radius = n

Volume	1563457.5663561
Surface area	65144.065264838
Circumference	452.38934211693

Square

Length = n

Perimeter	288
Area	5184
Diagonal	101.82337649086

Cube

Length = n

Surface area	31104
Volume	373248
Space diagonal	124.70765814496

Equilateral Triangle

Length = n

Perimeter	216
Area	2244.7378466093
Altitude	62.35382907248

Triangular Pyramid

Length = n

Surface area	2244.7378466093
Volume	43987.698644053
Height	33.941125496954