Question

5. Find all the factors of the given numbers. (a) 15 (b) 25 (c) 30 (d) 42 (e) 44 Express the following numbers as the product of the prime factors. (a) 18 (b) 24 (c) 75 (d) 90 (f) 275 (g) 625 (h) 150 540 (e) 210 (1) 945​

Answer 1

To find the factors of a number, determine all the numbers that can divide it evenly. Expressing a number as the product of its prime factors involves breaking it down into its prime factors.

Step-by-step explanation:

To find the factors of a number, we need to determine all the numbers that can divide the given number evenly without leaving a remainder. Let's find the factors of each number:

1. Factors of 15: 1, 3, 5, 15
2. Factors of 25: 1, 5, 25
3. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
4. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
5. Factors of 44: 1, 2, 4, 11, 22, 44

To express a number as the product of its prime factors, we need to break down the number into its prime factors. Let's express each number as the product of its prime factors:

1. Prime factors of 18: 2 × 3 × 3
2. Prime factors of 24: 2 × 2 × 2 × 3
3. Prime factors of 75: 3 × 5 × 5
4. Prime factors of 90: 2 × 3 × 3 × 5
5. Prime factors of 275: 5 × 5 × 11
6. Prime factors of 625: 5 × 5 × 5 × 5
7. Prime factors of 540: 2 × 2 × 3 × 3 × 3 × 5
8. Prime factors of 210: 2 × 3 × 5 × 7
9. Prime factors of 945: 3 × 3 × 3 × 5 × 7