Question

Розклади число на просты множники 2 способом:242, 312, 720 ТОЖЕ СРОЧНО

Answer 1

Пошаговое объяснение:

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Answer 2

242|2
121 |11
11|11
1|


312|2
156|3
52|2
26|2
13|13
1|


720|2
360|3
120|2
60|2
30|2
15|3
5|5
1

Answer 3

Давайте разложим числа 242, 312 и 720 на простые множители.

1. 242:

\[ 242 = 2 \times 121 \]

\[ 121 = 11 \times 11 \]

Таким образом, разложение 242 на простые множители: \(2 \times 11 \times 11\).

2. 312:

\[ 312 = 2 \times 156 \]

\[ 156 = 2 \times 78 \]

\[ 78 = 2 \times 39 \]

\[ 39 = 3 \times 13 \]

Таким образом, разложение 312 на простые множители: \(2 \times 2 \times 2 \times 3 \times 13\).

3. 720:

\[ 720 = 2 \times 360 \]

\[ 360 = 2 \times 180 \]

\[ 180 = 2 \times 90 \]

\[ 90 = 2 \times 45 \]

\[ 45 = 3 \times 15 \]

\[ 15 = 3 \times 5 \]

Таким образом, разложение 720 на простые множители: \(2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5\).

Теперь у вас есть разложение каждого из этих чисел на простые множители.

Answer 4

Prime Factorization of 242

To find the prime factorization of 242, we can start by dividing it by the smallest prime number, which is 2. If 242 is divisible by 2, we continue dividing until we can no longer divide evenly.

1. Divide 242 by 2: 242 ÷ 2 = 121 2. Since 121 is not divisible by 2, we move on to the next prime number, which is 3.

3. Divide 121 by 3: 121 ÷ 3 = 40.33 (not divisible) 4. Since 121 is not divisible by 3, we move on to the next prime number, which is 5.

5. Divide 121 by 5: 121 ÷ 5 = 24.2 (not divisible) 6. Since 121 is not divisible by 5, we move on to the next prime number, which is 7.

7. Divide 121 by 7: 121 ÷ 7 = 17.29 (not divisible) 8. Since 121 is not divisible by 7, we move on to the next prime number, which is 11.

9. Divide 121 by 11: 121 ÷ 11 = 11 (divisible) 10. We have reached a prime factor, which is 11.

Therefore, the prime factorization of 242 is 2 × 11.

Prime Factorization of 312

To find the prime factorization of 312, we can follow a similar process as above:

1. Divide 312 by 2: 312 ÷ 2 = 156 2. Divide 156 by 2: 156 ÷ 2 = 78 3. Divide 78 by 2: 78 ÷ 2 = 39 4. Since 39 is not divisible by 2, we move on to the next prime number, which is 3.

5. Divide 39 by 3: 39 ÷ 3 = 13 6. Since 13 is a prime number, we have reached the end of the prime factorization.

Therefore, the prime factorization of 312 is 2 × 2 × 2 × 3 × 13, which can be simplified as 2^3 × 3 × 13.

Prime Factorization of 720

To find the prime factorization of 720, we can follow a similar process as above:

1. Divide 720 by 2: 720 ÷ 2 = 360 2. Divide 360 by 2: 360 ÷ 2 = 180 3. Divide 180 by 2: 180 ÷ 2 = 90 4. Divide 90 by 2: 90 ÷ 2 = 45 5. Since 45 is not divisible by 2, we move on to the next prime number, which is 3.

6. Divide 45 by 3: 45 ÷ 3 = 15 7. Divide 15 by 3: 15 ÷ 3 = 5 8. Since 5 is a prime number, we have reached the end of the prime factorization.

Therefore, the prime factorization of 720 is 2 × 2 × 2 × 2 × 3 × 3 × 5, which can be simplified as 2^4 × 3^2 × 5.

I hope this helps! Let me know if you have any further questions.