Question

What is GCD of 104 and 143?* ​

Answer 1

GCD of 104 and 143 = 13

Given :

The numbers 104 and 143

To find :

GCD of 104 and 143

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 3 :

Write down the given numbers

The given numbers are 104 and 143

Step 2 of 3 :

Prime factorise the given numbers

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:104 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:52 \:\:}} \\ {\underline{\sf{2}}}&\underline{\sf{\:\:26 \:\:}} \\\underline{\sf{13}}&\underline{\sf{\:\:13\:\:}}\\\underline{\sf{}}& {\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

∴ 104 = 2 × 2 × 2 × 13

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{11}}}&{\underline{\sf{\:\:14 3 \:\:}}}\\ {\underline{\sf{13}}}&\underline{\sf{\:\:13 \:\:}} \\ {\underline{\sf{}}}&\ {\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

∴ 143 = 11 × 13

Step 3 of 3 :

Find GCD of 104 and 143

From the prime factorisation of 104 and 143 we observe that 13 is the greatest common divisor of 104 and 143

Hence GCD of 104 and 143 = 13

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Answer 2

Answer:

gcf, hcf, gcd (104; 143) = 13: greatest (highest) common factor (divisor), calculated.

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