Class X Math all chapters Question Solved NCERT

Class X Math Excercise 1.2 Solve

Q1. Express each number as a product of its prime factors:

(i) 140

Solution:
140 = 2 × 70
= 2 × 2 × 35
= 2 × 2 × 5 × 7$$\boxed{140 = 2^2 \times 5 \times 7}$$140=22×5×7​

অসমীয়া:
140 ৰ মৌলিক গুণনীয়ক = $2^2 × 5 × 7$22×5×7

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(ii) 156

Solution:
156 = 2 × 78
= 2 × 2 × 39
= 2 × 2 × 3 × 13$$\boxed{156 = 2^2 \times 3 \times 13}$$156=22×3×13​

অসমীয়া:
156 = $2^2 × 3 × 13$22×3×13

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(iii) 3825

Solution:
3825 = 5 × 765
= 5 × 5 × 153
= 5 × 5 × 3 × 51
= 5 × 5 × 3 × 3 × 17$$\boxed{3825 = 3^2 \times 5^2 \times 17}$$3825=32×52×17​

অসমীয়া:
3825 = $3^2 × 5^2 × 17$32×52×17

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(iv) 5005

Solution:
5005 = 5 × 1001
= 5 × 7 × 11 × 13$$\boxed{5005 = 5 \times 7 \times 11 \times 13}$$5005=5×7×11×13​

অসমীয়া:
5005 = $5 × 7 × 11 × 13$5×7×11×13

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(v) 7429

Solution:
7429 = 17 × 437
= 17 × 19 × 23$$\boxed{7429 = 17 \times 19 \times 23}$$7429=17×19×23​

অসমীয়া:
7429 = $17 × 19 × 23$17×19×23

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🔹 Q2. Find the LCM and HCF of the following pairs using prime factorisation:

(i) 26 and 91

Prime factors:
26 = 2 × 13
91 = 7 × 13

HCF = 13
LCM = 2 × 7 × 13 = 182

অসমীয়া:
HCF = 13, LCM = 182

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(ii) 510 and 92

Prime factors:
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23

HCF = 2
LCM = $2^2 × 3 × 5 × 17 × 23 = 23460$22×3×5×17×23=23460

অসমীয়া:
HCF = 2, LCM = 23460

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🔹 Q3. Find the LCM and HCF of 306 and 657 by prime factorisation.

Prime factors:
306 = 2 × 3 × 3 × 17
657 = 3 × 3 × 73

HCF = $3^2 = 9$32=9
LCM = $2 × 3^2 × 17 × 73 = 22338$2×32×17×73=22338

অসমীয়া:
HCF = 9
LCM = 22338

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🔹 Q4. Check whether 6ⁿ can end with digit 0 for any natural number n.

Solution:
6ⁿ = (2 × 3)ⁿ
To end with 0, number must contain factor 5.
But 6ⁿ has no factor 5.

👉 Therefore, 6ⁿ cannot end with 0.

অসমীয়া:
0 ত শেষ হ’বলৈ 5 গুণনীয়ক লাগিব।
6ⁿ ত 5 নাই।
👉 অসম্ভৱ।

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🔹 Q5. Explain why 7 × 11 × 13 + 13 is a composite number.

Solution:
7 × 11 × 13 + 13
= 13(7 × 11 + 1)
= 13 × 78

Since it has factors other than 1 and itself, it is composite.

অসমীয়া:
13 এটা সাধাৰণ গুণনীয়ক।
অতএব সংখ্যা সংযোজিত (Composite)।

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📌 Exam Tips (HSLC)

✔ Prime factorisation steps must be shown
✔ Write HCF & LCM clearly
✔ Proof questions = full marks if steps are neat
✔ Use index form (powers) correctly