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Factors and multiplesArithmeticElementary schoolabout 1:08

Find the greatest common factor of 36, 48, 72: animated lesson

A narrated, step-by-step factors and multiples video lesson with captions. Final answer: 12.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Greatest common factor
    Find the greatest common factor of 36, 48, 72.
  2. 2. Steps, part 1
    1. 36=22×32,48=24×3,72=23×3236 = 2^{2} \times 3^{2},\quad 48 = 2^{4} \times 3,\quad 72 = 2^{3} \times 3^{2}
      Prime factorization of each number
    2. 48=1×36+1236=3×12+048 = 1 \times 36 + 12 \\ 36 = 3 \times 12 + 0
      Euclidean algorithm for GCF(36, 48)
    3. gcd⁡(36,48)=12\gcd(36, 48) = 12
      The last non-zero remainder is the GCF
    4. 72=6×12+072 = 6 \times 12 + 0
      Euclidean algorithm for GCF(12, 72)
  3. 3. Steps, part 2
    1. gcd⁡(12,72)=12\gcd(12, 72) = 12
      The last non-zero remainder is the GCF
    2. 22×3=122^{2} \times 3 = 12
      Confirm with shared prime factors
  4. 4. The answer
    1212

    GCF(36, 48, 72) = 12

  5. 5. Check
    • 36 ÷ 12 = 3
    • 48 ÷ 12 = 4
    • 72 ÷ 12 = 6

Transcript

The problem. Here is the problem: Find the greatest common factor of 36, 48, 72. Find the greatest common factor (also called GCD or HCF) of the numbers.

Steps, part 1. Prime factorization of each number. Euclidean algorithm for GCF(36, 48). 48 equals 1 times 36 plus 12; 36 equals 3 times 12 plus 0. The last non-zero remainder is the GCF. Euclidean algorithm for GCF(12, 72). 72 equals 6 times 12 plus 0.

Steps, part 2. The last non-zero remainder is the GCF. Confirm with shared prime factors. Multiply the primes common to every number, each with its smallest exponent.

The answer. So the answer is 12. 12 is the largest whole number that divides every number exactly.

Check. 36 divided by 12 equals 3. 48 divided by 12 equals 4. 72 divided by 12 equals 6.

About factors and multiples

Find greatest common factors and least common multiples using prime factorisation.

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Find the greatest common factor of 36, 48, 72 (Lesson)