Question 1

We will find the prime factors for each number.

Step 1 — Prime factors of 140

Let's divide 140 by prime numbers. We start with the smallest prime, 2.

$140 \div 2 = 70$

$70 \div 2 = 35$

$35 \div 5 = 7$

$7 \div 7 = 1$

$\boxed{140 = 2 \times 2 \times 5 \times 7 = 2^2 \times 5 \times 7}$

Step 2 — Prime factors of 156

Let's divide 156 by prime numbers. We start with the smallest prime, 2.

$156 \div 2 = 78$

$78 \div 2 = 39$

$39 \div 3 = 13$

$13 \div 13 = 1$

$\boxed{156 = 2 \times 2 \times 3 \times 13 = 2^2 \times 3 \times 13}$

Step 3 — Prime factors of 3825

Let's divide 3825 by prime numbers. The sum of digits is 18, so it is divisible by 3.

$3825 \div 3 = 1275$

$1275 \div 3 = 425$

$425 \div 5 = 85$

$85 \div 5 = 17$

$17 \div 17 = 1$

$\boxed{3825 = 3 \times 3 \times 5 \times 5 \times 17 = 3^2 \times 5^2 \times 17}$

Step 4 — Prime factors of 5005

Let's divide 5005 by prime numbers. The number ends in 5, so it is divisible by 5.

$5005 \div 5 = 1001$

$1001 \div 7 = 143$

$143 \div 11 = 13$

$13 \div 13 = 1$

$\boxed{5005 = 5 \times 7 \times 11 \times 13}$

Step 5 — Prime factors of 7429

Let's divide 7429 by prime numbers. We try prime numbers like 17, 19, 23.

$7429 \div 17 = 437$

$437 \div 19 = 23$

$23 \div 23 = 1$

$\boxed{7429 = 17 \times 19 \times 23}$

Answer

(i) $140 = 2^2 \times 5 \times 7$ (ii) $156 = 2^2 \times 3 \times 13$ (iii) $3825 = 3^2 \times 5^2 \times 17$ (iv) $5005 = 5 \times 7 \times 11 \times 13$ (v) $7429 = 17 \times 19 \times 23$