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Byju's Answer
Standard VII
Mathematics
GCD using Long Division Method
Determine the...
Question
Determine the GCD of
√
729
−
√
324
and
√
32
×
√
18
using long division method.
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Solution
First, find the square roots using prime factorization.
729
=
3
6
⇒
√
729
=
√
3
6
=
3
3
=
27
324
=
2
×
2
×
3
×
3
×
3
×
3
⇒
√
324
=
√
(
2
×
3
×
3
)
2
=
2
×
9
=
18
∴
√
729
−
√
324
=
27
−
18
=
9
√
32
×
√
18
=
√
32
×
18
=
√
(
4
×
8
)
×
(
2
×
9
)
=
√
2
2
×
4
2
×
3
2
=
2
×
4
×
3
=
24
∴
GCD of
√
729
−
√
324
and
√
32
⋅
√
18
is equivalent to GCD of
9
and
24.
Using long division method,
GCD
=
3
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