Question 58: Prime Factorization of 640

 

🔢 Question 58: Prime Factorization of 640

Q58: Find the prime factorization of 640.

Options:
(a) 2 × 2 × 2 × 2 × 2 × 5
(b) 2 × 2 × 2 × 2 × 2 × 2 × 5
(c) 2 × 2 × 2 × 2 × 2 × 5 × 5
(d) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

📝 Step 1: Start dividing by the smallest prime (2)

We know 640 is even, so divide by 2 repeatedly until we cannot:

  1. 640 ÷ 2 = 320 ✅

  2. 320 ÷ 2 = 160 ✅

  3. 160 ÷ 2 = 80 ✅

  4. 80 ÷ 2 = 40 ✅

  5. 40 ÷ 2 = 20 ✅

  6. 20 ÷ 2 = 10 ✅

  7. 10 ÷ 2 = 5 ✅

Now we are left with 5, which is a prime number.

📝 Step 2: Write all prime factors

We divided by 2 seven times, and then we have 5 left.

640=2×2×2×2×2×2×2×5640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

✅ Or in exponent form:

640=27×5640 = 2^7 × 5

✅ Step 3: Match with the options

The correct answer is:

(d) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 ✅

💡 Quick Tip for Prime Factorization

  1. Start dividing by the smallest prime (2, then 3, 5, 7…)

  2. Keep dividing until the result is prime.

  3. Count the number of times each prime divides to write exponents.

Comments

Post a Comment

Popular posts from this blog

Question 59: Simple Interest Problem

  💰 Question 59: Simple Interest Problem Q59: In how many years does a sum of ₹1200 become ₹1800 at a simple interest rate of 5% per annum ? Options: (a) 10 years (b) 20 years (c) 15 years 📝 Step 1: Recall the simple interest formula Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) 100 \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} Simple Interest (SI) = 100 Principal (P) × Rate (R) × Time (T) ​ We are given: Principal P = 1200 P = 1200 P = 1200 Final Amount A = 1800 A = 1800 A = 1800 Rate R = 5 % R = 5\% R = 5% per annum 📝 Step 2: Find the simple interest SI = Amount − Principal = 1800 − 1200 = 600 \text{SI} = \text{Amount} - \text{Principal} = 1800 - 1200 = 600 SI = Amount − Principal = 1800 − 1200 = 600 ✅ So, the interest earned = ₹600 📝 Step 3: Use SI formula to find time S I = P × R × T 100 SI = \frac{P \times R \times T}{...
Read more

Question 60: Multiply by 0.01

  Question 60: Multiply by 0.01 Q60: 140.75 × 0.01 = ? 140.75 \times 0.01 = ? 140.75 × 0.01 = ? Options: (a) 140.75 (b) 14000.75 (c) 1.4075 (d) 0.14075 📝 Step 1: Understand multiplication by 0.01 Multiplying by 0.01 is the same as dividing by 100 . 140.75 × 0.01 = 140.75 100 140.75 \times 0.01 = \frac{140.75}{100} 140.75 × 0.01 = 100 140.75 ​ 📝 Step 2: Move the decimal Decimal moves 2 places to the left (because 0.01 = 1/100): 140.75 → 1.4075 140.75 \rightarrow 1.4075 140.75 → 1.4075 ✅ Step 3: Answer Answer: (c) 1.4075 ✅ 💡 Quick Tip Multiplying by 0.1 → move decimal 1 place left Multiplying by 0.01 → move decimal 2 places left Multiplying by 0.001 → move decimal 3 places left
Read more