Question

3. Determine the missing number in each prime factorization. a) 80 X 2 X 2 X 2 X 5 e) 4968 = 23 x 33 x b) 198 = 2 X 3 X X 11 f) 297 = 3 X 11 c) 1750 = 2 x 53 x g) 2639 = 7 XX 29 d) 665 = X 7 X 19 h) 1331 = 11​

Answer 1

The missing values in each of the given prime factorization are :

• 2
• 3
• 7
• 5
• 23
• 3
• 13
• 3

1.) 80 = __ × 2 × 2 × 2 × 5

• Let missing number = p
• 80 = p × 40
• p = 80 ÷ 40
• p = 2

2.) 198 = 2 × 3 × __ × 11

• Let missing value = p
• 198 = 66 × p
• p = 198 ÷ 66
• p = 3

3.) 1750 = 2 × 5³ × __

• Let missing value = p
• 1750 = 125 × 2 × p
• p = 1750 ÷ 250
• p = 7

4.) 665 = __ × 7 × 19

• Let missing value = p
• 665 = 133p
• p = 665 ÷ 133
• p = 5

5.) 4968 = 2³ × 3³ × __

• Let missing value = p
• 4968 = 8 × 27 × p
• 4968 = 216 × p
• p = 4968 ÷ 216 = 23

6.) 297 = __³ ×11

• Let missing value = p
• 297 ÷ 11 = p³
• 27 = p³
• Take the cube root of 27
• p = 3

7.) 2639 = 7 × __ × 29

• Let missing value = p
• 2639 = 203 × p
• p = 2639 ÷ 203 = 13

8.) 1331 = 11^p

• Let missing value = p
• 11 × 11 × 11 = 1331
• 11³ = 1331
• p = 3

Therefore, the value of p represents the missing value in the prime factorization given.

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