Video summary

☑️ Máximo Común Divisior de Monomios | Video 3

Main summary

Key takeaways

Educational

Main ideas / concepts

The video explains how to find the greatest common divisor (MCD/GCD) of three monomials by:

  1. Computing the GCD of the coefficients (the numerical parts).
  2. Computing the common variables, using the smallest exponent among them.
  3. Combining both results to form the final GCD monomial.

Methodology (step-by-step) for the GCD of monomials

A) GCD of the coefficients

Given coefficients: 15, 24, 36.

Process: repeatedly divide by prime factors—using the idea of “how many times all three numbers can be divided exactly.”

The video follows prime-factor logic in stages:

  • Check divisibility by 2:

    • Only 24 and 36 are divisible by 2 (15 is not).
    • Divide the divisible ones:
      • 24 → 12
      • 36 → 18
    • Check again:
      • 12 and 18 are divisible by 2
      • Divide again:
        • 12 → 6
        • 18 → 9
    • Check again:
      • 6 and 9: only 6 is divisible by 2 (9 is not), so stop.
    • Result: coefficient contribution from 2 is (2^1).

  • Check divisibility by 3:

    • All three original numbers 15, 24, 36 are divisible by 3.
    • Divide by 3:
      • 15 → 5
      • 24 → 8
      • 36 → 12
    • Check again for a second factor of 3:
      • 5 is not divisible by 3, so stop.
    • Result: coefficient contribution from 3 is (3^1).

  • Overall coefficient GCD:

    • Combine the common prime factors.
    • The subtitles conclude the usable final common coefficient is 3.

B) GCD of the variables (letters)

The GCD monomial includes only variables that appear in all three monomials.

Variables checked:

  • A: not present in all three → excluded
  • B: present in all three → included
  • C: not present in all three → excluded
  • X: not present in the first term → excluded

For the included variable (B), use the smallest exponent across the three monomials:

  • Exponents of B:
    • First term: 3
    • Second term: 2
    • Third term: 4
  • Smallest exponent is 2, so the GCD uses (B^2).

Final result

The video concludes that the greatest common divisor of the three monomials is:

  • (\;3B^2) (written as “3b squares” in the subtitles)

Speakers / sources featured

  • No specific individual speaker is identified in the subtitles.

Original video