Question

2.знайти НСД (12; 24), НСД (44; 132)3.знайти НСК (24; 36)НСК (15; 4)4.розкласти на прості множники число 55445. Перевірте чи є числа 308 і 585 взаємно простими​

Answer 1

Ответ:

Будет 245() 2875((2578

Answer 2

НСД (12, 24)

To find the greatest common divisor (НСД) of two numbers, we can use the Euclidean algorithm. The Euclidean algorithm works by repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder until the remainder is zero. The last non-zero remainder is the greatest common divisor of the two numbers.

Let's apply the Euclidean algorithm to find the НСД of 12 and 24:

Step 1: 24 divided by 12 equals 2 with a remainder of 0. Since the remainder is zero, the algorithm stops here, and the НСД of 12 and 24 is 12.

Therefore, НСД(12, 24) = 12.

НСД (44, 132)

Now, let's find the НСД of 44 and 132 using the Euclidean algorithm:

Step 1: 132 divided by 44 equals 3 with a remainder of 0. Since the remainder is zero, the algorithm stops here, and the НСД of 44 and 132 is 44.

Therefore, НСД(44, 132) = 44.

НСК (24, 36)

To find the least common multiple (НСК) of two numbers, we can use the formula:

НСК(a, b) = (a * b) / НСД(a, b)

Let's calculate the НСК of 24 and 36 using this formula:

НСД(24, 36) = 12 НСК(24, 36) = (24 * 36) / 12 = 864 / 12 = 72

Therefore, НСК(24, 36) = 72.

НСК (15, 4)

Now, let's find the НСК of 15 and 4 using the same formula:

НСД(15, 4) = 1 НСК(15, 4) = (15 * 4) / 1 = 60

Therefore, НСК(15, 4) = 60.

Розкласти на прості множники число 55445

To factorize the number 55445 into its prime factors, we can start by dividing it by the smallest prime number, which is 2. We continue dividing by prime numbers until we reach 1.

55445 divided by 2 equals 27722 with no remainder. 27722 divided by 2 equals 13861 with no remainder. 13861 divided by 7 equals 1980 with a remainder of 1. 1980 divided by 2 equals 990 with no remainder. 990 divided by 2 equals 495 with no remainder. 495 divided by 3 equals 165 with no remainder. 165 divided by 3 equals 55 with no remainder. 55 divided by 5 equals 11 with no remainder.

Therefore, the prime factorization of 55445 is 2 * 2 * 7 * 3 * 3 * 5 * 11 = 2^2 * 7 * 3^2 * 5 * 11.

Взаємна простота чисел 308 і 585

To check if two numbers, 308 and 585, are coprime (vzayemno prosti), we need to find their greatest common divisor (НСД). If the НСД is 1, then the numbers are coprime.

Let's calculate the НСД of 308 and 585 using the Euclidean algorithm:

Step 1: 585 divided by 308 equals 1 with a remainder of 277.

Step 2: 308 divided by 277 equals 1 with a remainder of 31.

Step 3: 277 divided by 31 equals 8 with a remainder of 13.

Step 4: 31 divided by 13 equals 2 with a remainder of 5.

Step 5: 13 divided by 5 equals 2 with a remainder of 3.

Step 6: 5 divided by 3 equals 1 with a remainder of 2.

Step 7: 3 divided by 2 equals 1 with a remainder of 1.

Step 8: 2 divided by 1 equals 2 with a remainder of 0.

Since the remainder is zero at the end, the НСД of 308 and 585 is 1. Therefore, the numbers 308 and 585 are coprime (vzayemno prosti).