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Factors and multiplesArithmeticElementary schoolabout 0:57

Find the greatest common factor of 84, 126: animated lesson

A narrated, step-by-step factors and multiples video lesson with captions. Final answer: 42.

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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. The problem
Greatest common factor
Find the greatest common factor of 84, 126.
2. Step by step
1. $84 = 2^{2} \times 3 \times 7,\quad 126 = 2 \times 3^{2} \times 7$
  Prime factorization of each number
2. $126 = 1 \times 84 + 42 \\ 84 = 2 \times 42 + 0$
  Euclidean algorithm for GCF(84, 126)
3. $\gcd(84, 126) = 42$
  The last non-zero remainder is the GCF
4. $2 \times 3 \times 7 = 42$
  Confirm with shared prime factors
3. The answer
$42$
GCF(84, 126) = 42
4. Check
- 84 ÷ 42 = 2
- 126 ÷ 42 = 3

Transcript

The problem. Here is the problem: Find the greatest common factor of 84, 126. Find the greatest common factor (also called GCD or HCF) of the numbers.

Step by step. Prime factorization of each number. Euclidean algorithm for GCF(84, 126). 126 equals 1 times 84 plus 42; 84 equals 2 times 42 plus 0. 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 42. 42 is the largest whole number that divides every number exactly.

Check. 84 divided by 42 equals 2. 126 divided by 42 equals 3.

About factors and multiples

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

Find the greatest common factor of 84, 126: Animated Lesson