Govt. Exams
Entrance Exams
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.
# Sum of Prime Numbers Between 10 and 25
To find the sum of prime numbers, we must first identify all prime numbers in the given range, then add them together.
Step 1: Identify All Prime Numbers Between 10 and 25
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We check each number in the range for primality.
(Note: 12, 14, 15, 16, 18, 20, 21, 22, 24 are composite; 10 and 25 are composite)
Step 2: Calculate the Sum
Adding all identified prime numbers together:
The sum of all prime numbers between 10 and 25 is 83.
Answer: (C) 83
If number is x, then (x × 3/4) ÷ (2/3) = (3x/4) × (3/2) = 9x/8. The factor is 9/8.
24 = 2³ × 3, 36 = 2² × 3². LCM = 2³ × 3² = 8 × 9 = 72.
91 = 7 × 13, so it's composite. 97, 89, and 83 are all prime numbers.
6³ = 216. Thus 216 is a perfect cube.
Let numbers be x and y. x + y = 50 and x - y = 10. Adding: 2x = 60, so x = 30.
Digit sum = 9 + 8 + 7 + 6 + 5 + 4 = 39.
Using Euclidean algorithm: 180 = 144×1 + 36; 144 = 36×4 + 0. Therefore HCF = 36.
Using the division algorithm: Number = (Divisor × Quotient) + Remainder. Number = (15 × 23) + 8 = 345 + 8 = 353.
