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Here is the problem: Find the greatest common factor of 105, 140.

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Find the greatest common factor (also called GCD or HCF) of the numbers.

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Prime factorization of each number.

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Euclidean algorithm for GCF(105, 140). 140 equals 1 times 105 plus 35; 105 equals 3 times 35 plus 0.

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The last non-zero remainder is the GCF.

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Confirm with shared prime factors. Multiply the primes common to every number, each with its smallest exponent.

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So the answer is 35.

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35 is the largest whole number that divides every number exactly.

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105 divided by 35 equals 3.

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140 divided by 35 equals 4.