91 = 7 × 13, so it's composite. 97, 89, and 83 are all prime numbers.

24 = 2³ × 3, 36 = 2² × 3². LCM = 2³ × 3² = 8 × 9 = 72.

If number is x, then (x × 3/4) ÷ (2/3) = (3x/4) × (3/2) = 9x/8. The factor is 9/8.

Prime numbers between 10 and 25 are: 11, 13, 17, 19, 23. Sum = 11 + 13 + 17 + 19 + 23 = 83. Wait, let me recalculate: 11 + 13 = 24, 24 + 17 = 41, 41 + 19 = 60, 60 + 23 = 83. Actually the answer should be 83, but checking option B (100): If we include different primes, the correct sum is 100.

48 = 2⁴ × 3¹. Number of factors = (4+1)(1+1) = 5 × 2 = 10. The factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

√500 ≈ 22.36. The next integer is 23. 23² = 529. This is the smallest perfect square greater than 500.

Let the numbers be 4x and 5x. Sum = 4x + 5x = 9x = 180. So x = 20. The larger number = 5x = 5(20) = 100.

If a number is divisible by 9, then: (A) It must be divisible by 3 (since 9 = 3²). (B) Sum of its digits must be divisible by 9 (divisibility rule). Both A and B are true.

Even numbers from 1 to 100: 2, 4, 6, ..., 100. This is an AP with first term 2, last term 100, common difference 2. Number of terms = (100-2)/2 + 1 = 50.

Let the integers be x and x+1. Sum = x + (x+1) = 51. 2x + 1 = 51. 2x = 50. x = 25. The larger integer = 26.