Integers Calculator

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Example

Created on 2024-06-20Asked by Elijah Smith (Solvelet student)

Find the greatest common divisor (GCD) of 56 and 98.

Solution

To find the greatest common divisor (GCD) of 56 and 98: Use the Euclidean algorithm, which involves repeated division: 1. Divide 98 by 56 and find the remainder. 2. Replace 98 with 56 and 56 with the remainder from step 1. 3. Repeat until the remainder is 0. First, divide 98 by 56:

98 \div 56 = 1 \text{ with a remainder of } 42

98 = 56 \cdot 1 + 42

Next, replace 98 with 56 and 56 with 42, and repeat:

56 \div 42 = 1 \text{ with a remainder of } 14

56 = 42 \cdot 1 + 14

Next, replace 56 with 42 and 42 with 14, and repeat:

42 \div 14 = 3 \text{ with a remainder of } 0

42 = 14 \cdot 3 + 0

The remainder is now 0, so the GCD is the last non-zero remainder, which is 14. Therefore, the greatest common divisor (GCD) of 56 and 98 is:

\text{GCD}(56, 98) = 14

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DefinitionIntegers are a set of whole numbers which may contain positive, negative, or no integer. These are labeled by Z and are the number systems used in an immense amount of math, such as algebra, number theory, and combinatorics. We can add, subtract and multiply integers, but we cannot divide. The dots are frequently used in theoretical mathematics, as a means to count and to order, and they are accordingly used as an example of a reserved character in applied mathematics. Example: Integer Set −...,−3,−2,−1,0,1,2,3,....

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