Question 20 of 36intermediate🔍 AnalyzeNumerical2 marks

How many three-digit prime numbers can you make using each of 2, 4 and 5 once?

Correct Answer

Step 1: Possible three-digit numbers using 2, 4, 5: 245, 254, 425, 452, 524, 542.

Step 2: Numbers ending in 2 or 4 are even, hence divisible by 2: 254, 452, 524, 542.

Step 3: Numbers ending in 5 are divisible by 5: 245, 425.

Step 4: All possible numbers are either even or divisible by 5.

Step 5: None of them can be prime.

∴ Zero three-digit prime numbers can be formed.

Exercise: Figure it Out (Section 3) | Q: 11 | (Page Page 9)
For More Understanding

Explanation

Using digits 2, 4, 5, we can form: 245, 254, 425, 452, 524, 542. All these numbers are even (ending in 2 or 4) or divisible by 5 (ending in 5). Numbers ending in 2 or 4 are divisible by 2. Numbers ending in 5 are divisible by 5. None can be prime.

Solution Steps

  1. Step 1: Possible three-digit numbers using 2, 4, 5: 245, 254, 425, 452, 524, 542.

  2. Step 2: Numbers ending in 2 or 4 are even, hence divisible by 2: 254, 452, 524, 542.

  3. Step 3: Numbers ending in 5 are divisible by 5: 245, 425.

  4. Step 4: All possible numbers are either even or divisible by 5.

  5. Step 5: None of them can be prime.

PreviousNext