Question

. Сколько делителей у числа 72? А) 10; В) 9; C) 11; D) 12.

Answer 1

D)12 72 делится на 1,2,3,4,6,8,9,12,18,24,36,72

Answer 2

Number of Divisors of 72

The number of divisors of a given number can be determined by finding its prime factorization and using the formula: (a+1)(b+1)(c+1)..., where a, b, c, etc. are the exponents of the prime factors.

Let's find the prime factorization of 72:

- 72 can be divided by 2: 72/2 = 36 - 36 can be divided by 2: 36/2 = 18 - 18 can be divided by 2: 18/2 = 9 - 9 can be divided by 3: 9/3 = 3 - 3 is a prime number and cannot be divided further.

Therefore, the prime factorization of 72 is 2^3 * 3^2.

Now, let's use the formula to find the number of divisors:

- The exponent of 2 is 3, so we have (3 + 1) = 4 factors of 2. - The exponent of 3 is 2, so we have (2 + 1) = 3 factors of 3.

Multiplying these numbers together, we get (4 * 3) = 12.

Therefore, the number 72 has 12 divisors.

Answer:

The number of divisors of 72 is 12.