Express the following number as a product of its prime factor: 7429

• a) 11 × 19 × 23
• b) 17 × 19 × 23
• c) 17 × 23 × 23
• d) 17 × 19 × 29

To express the number 7429 as a product of its prime factors, we need to break it down into its prime components. This involves dividing the number by prime numbers until we can no longer divide evenly. Let's go through the process step by step.

Finding Prime Factors

First, we can start by checking if 7429 is divisible by the smallest prime numbers: 2, 3, 5, 7, and so on.

• Divisibility by 2: 7429 is odd, so it's not divisible by 2.
• Divisibility by 3: The sum of the digits (7 + 4 + 2 + 9 = 22) is not divisible by 3.
• Divisibility by 5: The last digit is not 0 or 5, so it's not divisible by 5.
• Divisibility by 7: 7429 ÷ 7 = 1061.2857 (not divisible).
• Divisibility by 11: 7429 ÷ 11 = 675.3636 (not divisible).
• Divisibility by 13: 7429 ÷ 13 = 572.2308 (not divisible).
• Divisibility by 17: 7429 ÷ 17 = 436.4118 (not divisible).
• Divisibility by 19: 7429 ÷ 19 = 390.4737 (not divisible).
• Divisibility by 23: 7429 ÷ 23 = 323.4348 (not divisible).
• Divisibility by 29: 7429 ÷ 29 = 256.8621 (not divisible).
• Divisibility by 37: 7429 ÷ 37 = 200.7879 (not divisible).
• Divisibility by 41: 7429 ÷ 41 = 181.9024 (not divisible).
• Divisibility by 43: 7429 ÷ 43 = 172.1860 (not divisible).
• Divisibility by 47: 7429 ÷ 47 = 158.8511 (not divisible).
• Divisibility by 53: 7429 ÷ 53 = 140.5660 (not divisible).
• Divisibility by 59: 7429 ÷ 59 = 126.9492 (not divisible).
• Divisibility by 61: 7429 ÷ 61 = 121.9672 (not divisible).
• Divisibility by 67: 7429 ÷ 67 = 110.7463 (not divisible).
• Divisibility by 71: 7429 ÷ 71 = 104.0141 (not divisible).
• Divisibility by 73: 7429 ÷ 73 = 101.0959 (not divisible).
• Divisibility by 79: 7429 ÷ 79 = 94.9494 (not divisible).
• Divisibility by 83: 7429 ÷ 83 = 89.6590 (not divisible).
• Divisibility by 89: 7429 ÷ 89 = 83.1461 (not divisible).
• Divisibility by 97: 7429 ÷ 97 = 76.1443 (not divisible).
• Divisibility by 101: 7429 ÷ 101 = 73.1683 (not divisible).
• Divisibility by 103: 7429 ÷ 103 = 72.0592 (not divisible).
• Divisibility by 107: 7429 ÷ 107 = 69.4850 (not divisible).
• Divisibility by 109: 7429 ÷ 109 = 68.1743 (not divisible).
• Divisibility by 113: 7429 ÷ 113 = 65.7035 (not divisible).
• Divisibility by 127: 7429 ÷ 127 = 58.2677 (not divisible).
• Divisibility by 131: 7429 ÷ 131 = 56.7030 (not divisible).
• Divisibility by 137: 7429 ÷ 137 = 54.3140 (not divisible).
• Divisibility by 139: 7429 ÷ 139 = 53.3885 (not divisible).
• Divisibility by 149: 7429 ÷ 149 = 49.5872 (not divisible).
• Divisibility by 151: 7429 ÷ 151 = 49.0000 (divisible).

After testing various primes, we find that 7429 is divisible by 151. Dividing gives us:

7429 ÷ 151 = 49

Breaking Down the Result

Now, we need to factor 49, which is a perfect square:

49 = 7 × 7

Final Prime Factorization

Putting it all together, we have:

7429 = 151 × 7 × 7

In terms of the options provided:

• a) 11 × 19 × 23
• b) 17 × 19 × 23
• c) 17 × 23 × 23
• d) 17 ×