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Factors and multiplesArithmeticElementary schoolabout 0:57

Find the greatest common factor of 105, 140: animated lesson

A narrated, step-by-step factors and multiples video lesson with captions. Final answer: 35.

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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 105, 140.
2. Step by step
1. $105 = 3 \times 5 \times 7,\quad 140 = 2^{2} \times 5 \times 7$
  Prime factorization of each number
2. $140 = 1 \times 105 + 35 \\ 105 = 3 \times 35 + 0$
  Euclidean algorithm for GCF(105, 140)
3. $\gcd(105, 140) = 35$
  The last non-zero remainder is the GCF
4. $5 \times 7 = 35$
  Confirm with shared prime factors
3. The answer
$35$
GCF(105, 140) = 35
4. Check
- 105 ÷ 35 = 3
- 140 ÷ 35 = 4

Transcript

The problem. Here is the problem: Find the greatest common factor of 105, 140. 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(105, 140). 140 equals 1 times 105 plus 35; 105 equals 3 times 35 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 35. 35 is the largest whole number that divides every number exactly.

Check. 105 divided by 35 equals 3. 140 divided by 35 equals 4.

About factors and multiples

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

Find the greatest common factor of 105, 140: Animated Lesson