High School

We appreciate your visit to Complete the Table Number s Prime factors HCF LCM 8 10 2x2x2 2 3 2x2x3 2 2 x 3 2 2 4 2 3 x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Complete the Table

| Number's | Prime factors | HCF | LCM |
|---|---|---|---|
| 8, 10 | 2x2x2 = 2^3, 2x2x3 = 2^2 x 3 | 2^2 = 4 | 2^3 x 3 = 24 |
| 9, 15 | 3x3 = 3^2, 3x3x3x3x3 = 3^5 | 3^5 = | 3^2 x 2 = |
| 10, 24 | 5x3 = 5^2, 2x12 = 2x12 | | |
| 16, 08 | 4x4 = 4^2 | | 4^2 x 2 = |
| 27, 36 | 3x3x3 = 3^3, 12x12x12 = 12^3 | 12^3 = | 3^3 x 3 = |
| 39, 65, 140 | | | |

Answer :

To complete the given table, we need to find the prime factors, highest common factor (HCF), and least common multiple (LCM) for each set of numbers listed. Let's go through each pair step-by-step:

  1. For 9 and 15:

    • Prime Factors:
      • 9 = 3 \times 3 = 3^2
      • 15 = 3 \times 5
    • HCF:
      • The highest common factor is the highest power of the common prime factor. Here, the common prime factor is 3. Therefore, HCF = 3^1 = 3.
    • LCM:
      • Take each prime number appearing in any factorization to the highest power,
        • LCM = 3^2 \times 5 = 45.

  2. For 10 and 24:

    • Prime Factors:
      • 10 = 2 \times 5
      • 24 = 2^3 \times 3
    • HCF:
      • The common prime factor is 2. Therefore, HCF = 2^1 = 2.
    • LCM:
      • LCM = 2^3 \times 3 \times 5 = 120.

  3. For 16 and 08:

    • Prime Factors:
      • 16 (which should be paired with another number like 8) = 2^4
      • 8 = 2^3
    • HCF:
      • HCF = 2^3 = 8.
    • LCM:
      • LCM = 2^4 = 16.

  4. For 27 and 36:

    • Prime Factors:
      • 27 = 3^3
      • 36 = 2^2 \times 3^2
    • HCF:
      • The common prime factor is 3. Therefore, HCF = 3^2 = 9.
    • LCM:
      • LCM = 2^2 \times 3^3 = 108.

  5. For 39, 65, and 140:

    • Prime Factors:
      • 39 = 3 \times 13
      • 65 = 5 \times 13
      • 140 = 2^2 \times 5 \times 7
    • HCF:
      • Here, there is no common factor among all three numbers, so HCF = 1.
    • LCM:
      • LCM = 2^2 \times 3 \times 5 \times 7 \times 13 = 2730.

Remember, the HCF is found by choosing the smallest power of common primes, while the LCM involves taking each prime number found in any of the numbers to its highest power.

Thanks for taking the time to read Complete the Table Number s Prime factors HCF LCM 8 10 2x2x2 2 3 2x2x3 2 2 x 3 2 2 4 2 3 x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada