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EXERCISE 11
nd . Use Buclid's division algorithm to find the HCF of:
@ 135 and 225
(1) 196 and 38220
(m) 867 and 255
2. Show that any positive odd integer is of the form 64 + 1. or 64 +3. or 64 +5.where is
Sale 2. Show tha
some integer.
Anarmy contingent of 616 members is to march behind an army band of 32 members in
parade. The two groups are to march in the same number of columns. What is the
maximum number of columns in which they can march?
4. Use Euclid's division lemma to show that the square of any positive integer is either of
the form 3m or 3m + 1 for some integer m.
+3 [Hint: Letxbe any positive integer then it is of the form 39,34 + 1 or 3q +2. Now square
each of these and show that they can be rewritten in the form 3m or 3m +1.]
5. Use Euclid's division lemma to show that the cube of any positive integer is of the for
app9m. 9m + 1 or 9m+8.
3 The Fundamental Theorem of Arithmetic
vour earlier classes, you have seen that any natural number can be written asshow that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6 Cube + 5 Where Q is some integer ​

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