Is 279 a Prime Number?

No, the integer 279 is not a prime number. The prime number should follow the 2 important protocols,

 v_rocket O3

• Greater than 1
• Contains only 2 factors.

Based on the above rules, the number 279 is greater than one. The number is divisible by 1,3,9,31,93,279. So, the integer 279  has 6 factors. Hence, proved that the number 279 is not a prime number.

Formula for square root:

a2 + b2  =  c2

To check if the number is a prime number or not, we are following 3 different methods. They are,

• Basic Division Test,
• Adding and subtracting numbers from left to right
• Advance Prime Testing Algorithm.

Let's see these methods in detail.

Method 1: Basic Division Test

Basic division methods involve different steps to check if the number is prime number or not. They are,

Step 1 - Take the square root for the number 279

Step 2 - Divide the number 279 by each prime number up to its square root. List out the prime number below 16 - 2,3,5,7,11,13.

Step 3 - Now we are going to utilize the divisibility check to see if the number is a prime number or not.

Divisibility check by 2  - According to the rule, the last digit of the number 279 is not an even number. Hence the number 279 is not divided by 2.

Divisibility check by 3 - According to the divisibility check rule 3, The number 279 was separated into each digit, (i.e) 2,7,9. The sum of integer 2+7+9 = 18. The number 18 is divisible by 3. Hence, the number 279 is divided by 3. The number 279/3 = 93

Divisibility check by 5 - According to the divisibility check rule 5, the last digit if the number is 5 or 0. The number 279 was not divided by 5. Because the last digit of the number 279 is 9.

Divisibility check by 7 - According to the divisibility check rule 7, Multiply the number 9 by 2 which results in 18. Subtract the number 27 by 18 which results in 9. We know that the number 9 is not a multiple of 7. The number 279 is not divided by 7.

Divisibility check by 11 - According to the divisibility check rule 11, 2+9 = 11. Find the difference between 11 - 7 = 4. Hence the number is not divisible by 11.

Divisibility check by 13 - According to the divisibility rule 13, Multiply the last digit of the number by 279 by 4 (i.e) 9 X 4 = 36. Add the result to the rest of the number 27 + 36 =63. Hence , the number 63 is not divided by 13.

Method 2: Adding and subtracting numbers from left to right

Step 1 - Split the number into separate digits like 2,7,9.

Step 2 - Add and subtract the numbers alternatively (i.e) 2 - 7 + 9 =4

Step 3 -  The result should be divided by 7,11,13.

Step 4 - The number is not divided by 7,11,13.

Method 3: Advanced Prime Testing Algorithms

The Advanced Prime Testing Algorithm is used for only large numbers. There are different primality testing algorithms but here we use trial division algorithms which is the same as basic division algorithm.

Divisibility check by 2  - According to the rule, the last digit of the number 279 is not an even number. Hence the number 279 is not divided by 2.

Divisibility check by 3 - According to the divisibility check rule 3, The number 279 was separated into each digit, (i.e) 2,7,9. The sum of integer 2+7+9 = 18. The number 18 is divisible by 3. Hence, the number 279 is divided by 3. The number 279/3 = 93.

Hence, the number 279 is not a prime number.

The factors of 279 are the 1,3,9,31,93,279. The number 279 can be divided into the number 1,3,9,31,93,279. The factors can be calculated by multiplication or division.

The number 279 is not a prime number. Hence, it cannot be classified under the prime numbers.Let discuss the classification of prime numbers. They are, 

• Twin prime numbers, 
• Sophie Prime Numbers, 
• Mersenne Numbers,
• Wilson prime numbers.

279 is not a prime number. So, the number 279 can’t be classified under these prime numbers.

The number 279 is not a prime number. Hence there are no properties. But as a composite number it has a lot of properties and will discuss it in the next segment.

Yes, the number 279 is a composite number because it has more than two factors. The factors are 1,3,9,31,93,279.

The number 279 is not  a square number. By using the square tables, we can check if the number is square number or not?

The square root of the number 279 is 16.70. The square root of the number 279  lies between the number 16 and 17.

The other interesting facts about 279,

• 279 is a composite number.
• It is the sequence of Harshad’s Number.
• The number 279 is considered as the sum of two squares (i.e) 62 + 152 = 279.
• Asteroid 279 Thule  is the largest asteroid  in the asteroid belt.
• 279 Hz can be used as a frequency for tuning or creating specific soundscapes.

Comparing the three methods, 

The best method is the basic division method and the trial division methods. Because these two methods give the accurate result.

The 2nd method: Adding and subtracting numbers from left to right used for metal calculations. But it doesn’t give accurate results like the basic division method.

We concluded that the number 279 is not a prime number. We proved the above statement by using different methods. Through this topic, we learned about the factors of the given number and how to find the square root of the given number. By using these tips and tricks, the student can determine whether the number is a prime number or not.