Find the greatest number that exactly divides $513, 1134$ and $1215$ .

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Solution

Find the HCF
Given numbers: $513, 1134$ and $1215$ .
Prime factorization of $513 = 3 x 3 x 3 x 19$
Prime factorization of $1134 = 2 x 3 x 3 x 3 x 3 x 7$
Prime factorization of $1215 = 3 x 3 x 3 x 3 x 3 x 5$
HCF $(513, 1134, 1215) = 3 \times 3 \times 3 = 27$
Hence, the greatest number that divides $513, 1134$ and is $27$ .

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