Answer :
To find a prime number between [tex]\(50 \frac{2}{3}\)[/tex] and [tex]\(57 \frac{3}{4}\)[/tex], let's start by converting these mixed fractions into improper fractions or decimals for clear bounds:
- [tex]\(50 \frac{2}{3} = 50 + \frac{2}{3} = 50 + 0.6667 \approx 50.67\)[/tex]
- [tex]\(57 \frac{3}{4} = 57 + \frac{3}{4} = 57 + 0.75 = 57.75\)[/tex]
So, we are looking for prime numbers strictly between 50.67 and 57.75. The whole numbers in this range are 51, 52, 53, 54, 55, 56, and 57. Let's check which of these are prime numbers:
1. 51:
- 51 is not a prime number because it is divisible by 3 (51 ÷ 3 = 17).
2. 52:
- 52 is not a prime number because it is divisible by 2 (52 ÷ 2 = 26).
3. 53:
- Let's check if 53 is a prime number.
- 53 is not divisible by 2 (it's odd).
- 53 is not divisible by 3 (5 + 3 = 8, which is not divisible by 3).
- 53 is not divisible by 5 (the last digit is not 0 or 5).
- We can check up to the square root of 53 (approximately 7.28), so we should also check 7:
- 53 ÷ 7 ≈ 7.5714 (not a whole number).
- Therefore, 53 is not divisible by any number other than 1 and itself, making it a prime number.
4. 54:
- 54 is not a prime number because it is divisible by 2 (54 ÷ 2 = 27).
5. 55:
- 55 is not a prime number because it is divisible by 5 (55 ÷ 5 = 11).
6. 56:
- 56 is not a prime number because it is divisible by 2 (56 ÷ 2 = 28).
7. 57:
- 57 is not a prime number because it is divisible by 3 (57 ÷ 3 = 19).
Among the numbers 51, 52, 53, 54, 55, 56, and 57, only 53 is a prime number.
Therefore, the prime number between [tex]\(50 \frac{2}{3}\)[/tex] and [tex]\(57 \frac{3}{4}\)[/tex] is:
[tex]\[
\boxed{53}
\][/tex]
- [tex]\(50 \frac{2}{3} = 50 + \frac{2}{3} = 50 + 0.6667 \approx 50.67\)[/tex]
- [tex]\(57 \frac{3}{4} = 57 + \frac{3}{4} = 57 + 0.75 = 57.75\)[/tex]
So, we are looking for prime numbers strictly between 50.67 and 57.75. The whole numbers in this range are 51, 52, 53, 54, 55, 56, and 57. Let's check which of these are prime numbers:
1. 51:
- 51 is not a prime number because it is divisible by 3 (51 ÷ 3 = 17).
2. 52:
- 52 is not a prime number because it is divisible by 2 (52 ÷ 2 = 26).
3. 53:
- Let's check if 53 is a prime number.
- 53 is not divisible by 2 (it's odd).
- 53 is not divisible by 3 (5 + 3 = 8, which is not divisible by 3).
- 53 is not divisible by 5 (the last digit is not 0 or 5).
- We can check up to the square root of 53 (approximately 7.28), so we should also check 7:
- 53 ÷ 7 ≈ 7.5714 (not a whole number).
- Therefore, 53 is not divisible by any number other than 1 and itself, making it a prime number.
4. 54:
- 54 is not a prime number because it is divisible by 2 (54 ÷ 2 = 27).
5. 55:
- 55 is not a prime number because it is divisible by 5 (55 ÷ 5 = 11).
6. 56:
- 56 is not a prime number because it is divisible by 2 (56 ÷ 2 = 28).
7. 57:
- 57 is not a prime number because it is divisible by 3 (57 ÷ 3 = 19).
Among the numbers 51, 52, 53, 54, 55, 56, and 57, only 53 is a prime number.
Therefore, the prime number between [tex]\(50 \frac{2}{3}\)[/tex] and [tex]\(57 \frac{3}{4}\)[/tex] is:
[tex]\[
\boxed{53}
\][/tex]
