Express Numbers as Product of Prime Factors

 

❓ Question

Express each number as a product of its prime factors:

(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429

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🖼️ Solution Image

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✍️ Short Solution

This is a prime factorisation question.
Keep dividing the number by the smallest possible prime number until 1 is obtained 💯

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🔹 Step 1 — Prime Factorisation of 140

$$140 = 2 \times 70$$
$$70 = 2 \times 35$$
$$35 = 5 \times 7$$

Therefore,

$$140 = 2^2 \times 5 \times 7$$

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🔹 Step 2 — Prime Factorisation of 156

$$156 = 2 \times 78$$
$$78 = 2 \times 39$$
$$39 = 3 \times 13$$

Therefore,

$$156 = 2^2 \times 3 \times 13$$

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🔹 Step 3 — Prime Factorisation of 3825

$$3825 = 5 \times 765$$
$$765 = 5 \times 153$$
$$153 = 3 \times 51$$
$$51 = 3 \times 17$$

Therefore,

$$3825 = 3^2 \times 5^2 \times 17$$

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🔹 Step 4 — Prime Factorisation of 5005

$$5005 = 5 \times 1001$$
$$1001 = 7 \times 143$$
$$143 = 11 \times 13$$

Therefore,

$$5005 = 5 \times 7 \times 11 \times 13$$

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🔹 Step 5 — Prime Factorisation of 7429

$$7429 = 17 \times 437$$
$$437 = 19 \times 23$$

Therefore,

$$7429 = 17 \times 19 \times 23$$

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✅ Final Answer

$$140 = 2^2 \times 5 \times 7$$
$$156 = 2^2 \times 3 \times 13$$
$$3825 = 3^2 \times 5^2 \times 17$$
$$5005 = 5 \times 7 \times 11 \times 13$$
$$7429 = 17 \times 19 \times 23$$

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⭐ Key Insight

• Always divide by the smallest prime number first
• Continue till quotient becomes 1

🧠 Memory Line:

Prime factorisation = breaking a number into only prime numbers