A Story of Numbers — Class 8 solved problems

7 problems from this chapter, each solved step by step.

1. Icm kasa karna hai question 1024 sath ma solve karna hai

   Prime factorization: 1024 = 2^(10). To find the LCM, provide the other number(s) to compare the highest powers of all prime factors.

2. Prove that the sum of two odd numbers is always even

   The sum of two odd numbers is always an even number.

3. The remainder when (64^(64))^(64) is divided by 7 is equal to:

   1

4. Let m and n, (m<n) be two 2-digit numbers. Then the total number of pairs (m,n) such that (m,n)=6 is:

   84

5. Prove that among any 51 integers chosen from 1, 2,..., 100, there exist two that are coprime.

   Among any 51 integers chosen from 1, 2,..., 100, there exist two that are coprime.

6. The remainder, when 7^(103) is divided by 23, is equal to:

   14

7. To prove: n N (n+1)/(2) N ⇒ m N: n = 2m + 1. (natural numbers, proof, implication, existence, odd number)

   Given n N and (n+1)/(2) N. Let k = (n+1)/(2). Since k N, k is a natural number. Multiplying by 2, we get n+1 = 2k. Subtracting 1, we get n = 2k - 1. We want to

More Class 8 chapters

• A Square and A Cube1 solved
• Power Play3 solved
• Quadrilaterals3 solved
• Number Play1 solved
• We Distribute, Yet Things Multiply1 solved
• Proportional Reasoning-114 solved
• The Baudhayana-Pythagoras Theorem4 solved
• Proportional Reasoning-22 solved
• Exploring Some Geometric Themes2 solved
• Algebra Play4 solved
• Area2 solved

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