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. Q.2: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
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(i) 140
140=2×70
=2×2×35
=2×2×5×7
=2×2×5×7×1
(ii) 156
156=2×78
=2×2×39
=2×2×3×13
=2×2×3×13×1
(iii) 3825
3825=3×1275
=3×3×425
=3×3×5×85
=3×3×5×5×17
=3×3×5×5×17×1
(iv) 5005
5005=5×1001
=5×7×143
=5×7×11×13
=5×7×11×13×1
(v) 7429
7429=17×437
=17×19×23
=17×19×23×1(i) 140
140=2×70
=2×2×35
=2×2×5×7
=2×2×5×7×1
(ii) 156
156=2×78
=2×2×39
=2×2×3×13
=2×2×3×13×1
(iii) 3825
3825=3×1275
=3×3×425
=3×3×5×85
=3×3×5×5×17
=3×3×5×5×17×1
(iv) 5005
5005=5×1001
=5×7×143
=5×7×11×13
=5×7×11×13×1
(v) 7429
7429=17×437
=17×19×23
=17×19×23×1
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