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.

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