How To Find Out Prime Numbers Between 1 And 100

Prime and Composite Numbers

A blended number can exist made by multiplying two smaller whole numbers together.

For example 6 can exist made from 2 × 3.

We tin say that blended numbers can be broken down into other whole numbers.

Both 2 and three are different numbers to 6 and they are both smaller.

Because 6 can be cleaved downward, nosotros say that it is a composite number. It is composed of two times 3. half dozen is in the two times table and half-dozen is in the three times table.

Not all numbers can exist made past multiplying two smaller whole numbers.

Prime number numbers are numbers that cannot exist made by multiplying two smaller whole numbers.

Prime numbers are not in the times tables of any other numbers.

7 is an example of a prime.

The word prime also means 'first'. A prime is the first number in a times tabular array equally long as it does not announced in another times tabular array.

7 is not in any other times table apart from the 7 times tabular array.

7 can only exist written as i × 7. It cannot be broken downwardly into any smaller whole numbers.

Factors are the numbers that multiply together to make a larger number.

seven only has two factors, one and 7.

We say that prime numbers have exactly two factors, the number i and the number itself.

Apart from the number 1, every number is a prime number number or a composite number.

A number that is not a blended number is prime number and a number that is non a prime number is a composite number.

The number 1 is neither prime nor composite.

Prime numbers are not easy to find or identify.

The prime numbers to 100 are: 2, iii, 5, seven, 11, xiii, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

How to Find Prime Numbers

For a number to be prime information technology cannot be a multiple of any other smaller whole number.

To decide if a number is prime, divide it past all smaller prime numbers.

If any of the other smaller prime numbers carve up into our number exactly, so it is non prime.

If all of the smaller prime numbers do not split exactly into our number, then it is prime number.

Use the following rules to decide if a number is prime:

• Apart from 2 and v, all prime numbers will end in 1, 3, seven or 9.
• Apart from 2 and iii, all prime numbers are one more or 1 less than a number in the 6 times table.
• A prime won't exist in the times table of any other prime which is smaller than the square root of the number we are checking.

In this lesson we will expect farther at these rules using some examples.

We will first look at the number two. Two is the only even prime number.

2 can but be written as 1 × ii.

A prime is the first number in a times tabular array. 2 is the first number in the two times table and therefore it is prime number.

This ways that all other numbers in the two times table are not prime.

It is easy to check if a number is in the two times table. All numbers in the two times table end in a 2, iv, 6, 8 or 0.

So if a number ends in a ii, iv, half-dozen, 8 or 0, information technology is in the two times table and therefore is not a prime number.

For instance 4 is 2 × two and then, it is not prime.

6 is 2 × 3 and and so, it is not prime.

8 is 2 × iv and so, it is not prime.

10 is 2 × 5 and so, it is non prime number.

All numbers that stop in a two, 4, six, 8 or 0 are in the 2 times table and are not prime. This rule applies to all numbers, no matter how large.

twenty ends in a zero and therefore it is in the two times tabular array and is not prime.

82 ends in a 2 and then, is in the two times table and is not prime.

Here are the prime numbers to 100.

We can meet that apart from 2 and 5, all other prime numbers end in a 1, iii, 7 or nine.

From the digits 1, 2, 3, iv, 5, 6, 7, 8, nine and 0, we can already remove the digits of ii, iv, 6, 8 and 0 considering these are numbers in the 2 times table.

Nosotros are left with 1, 3, 5, 7, ix and 0.

Every number ending in 5 or 0 is besides in the 5 times tabular array and will never exist prime.

This leaves us with the digits of 1, 3, 7 and 9.

Not all numbers ending in ane, 3, seven and 9 are prime. For example 99 is 9 × 11 and so is non prime.

Even so, this rule allows u.s.a. to easily check if a number is not prime.

For case 35 ends in a v.

We know that apart from 2 and 5, larger prime numbers only end in a 1, 3, 7 or 9. 35 ends in a v and then, information technology cannot exist prime.

We will at present put all of our prime numbers to 100 on a number grid.

There is no pattern to the prime numbers and so they tin be difficult to find.

We tin can run across that apart from two and 3, all of the prime numbers are immediately next to a number in the 6 times table.

All prime numbers larger than three are one more than or one less than a number in the six times table.

Whatever number in the six times table plus two or plus 4 volition still exist even and therefore volition be in the two times tabular array.

Whatever number in the 6 times table plus 3 is still in the three times table.

This leaves the numbers that are one more or one less than a number in the vi times table.

For example, 43 is a prime number number. It is one more than 42, which is in the six times tabular array.

59 is also a prime number. It is one less than 60, which is in the six times tabular array.

This means that if a number is adjacent to a number in the 6 times tabular array and likewise ends in a i, 3, 7 or 9, it is very likely to be a prime.

However, not all numbers that end in 1, 3, vii and 9 are prime numbers.

Hither are some exceptions to be aware of.

49 is 7 × vii then it is not prime, fifty-fifty though information technology ends in a 9.

77 is 7 × xi and then information technology is not prime, fifty-fifty though information technology ends in a seven.

91 is vii × 13 and so it is non prime, fifty-fifty though information technology ends in a 1.

So if a number ends in 1, 3, 7 or nine and it is 1 more or less than a number in the 6 times table, and then it might be prime.

We still need to check each number to see if it really is prime number.

A prime number cannot be in the times table of any other smaller number and therefore, it cannot exist divided exactly past whatever other smaller number.

We tin divide smaller numbers into our prime to check if they divide in exactly or not.

Fortunately nosotros do non demand to try dividing past every smaller number.

We merely need to try dividing by prime numbers that are smaller than the square root of out number.

To check if a number is prime, split past prime numbers less than the square root of the number.

The square root is the number that multiplies past itself to give the original number.

Here we accept the number 31. It ends in a 1 and information technology is one more than 30, which is in the half dozen times table. It might exist prime then we volition test information technology.

We exercise non know the square root of 31 but nosotros know that 6 × 6 = 36. The square root of 36 is 6 and so we volition effort dividing past the prime numbers less than six.

These are 2, 3 and 5. We divide 31 by ii, 3 and five. If 2, 3 or 5 split exactly into 31, so 31 is non prime. If they do not dissever exactly, then 31 is prime

31 is odd and so 31 cannot be divided exactly by 2.

31 too cannot exist divided by 3 or 5 exactly.

Therefore 31 is prime.

Hither is an example of deciding if 27 is prime.

We try to divide by prime numbers smaller than the foursquare root of the number.

We do not know the foursquare root of 27 simply we know that 5 × 5 = 25. The square root of 25 is 5, and so we will endeavor dividing past ii, 3 and 5.

27 cannot be divided past 2 because information technology is odd.

27 can exist divided by three. 27 ÷ 3 = 9.

We can also tell that 27 is divisible by three by adding the digits. 2 + 7 = 9, which is in the three times table and so 27 is in the three times table.

27 is not prime number.

You may accept noticed that 27 is besides non 1 more or less than a number in the 6 times tabular array and therefore is not prime number.

Here is an example of xix, which ends in a 9 and is ane more than 18, which is in the vi times table.

We do not know the square root of xix but v × 5 = 25, so we can try dividing by prime numbers less than v.

19 cannot exist divided past 2 because xix is odd.

19 is not in the 3 times table because 1 + ix = x, which is not in the three times tabular array.

19 is not in the 5 times table because information technology does not cease in a 5 or 0.

Considering 19 is non divisible by 2, iii or 5, it is a prime number. Nosotros have tried dividing by all of the other prime numbers less than the square root of xix.

Hither is 61, which ends in a 1 and is ane more than threescore.

We know that 8 × 8 = 64, so nosotros can split 61 past all of the prime numbers less than 8.

We volition split 61 by ii, 3, 5 and 7.

61 is odd and and so, does not split up by ii exactly.

half dozen + 1 = 7, which is non in the three times table and so, 61 is non in the 3 times table.

61 ends in a 1. To exist in the 5 times table, a number must end in 5 or 0 and and then 61 is non divisible by 5.

61 is not divisible past 3. You might know that 63 is seven × ix and this helps us realise that 61 is not in the 7 times table.

61 is not divisible past 2, three, five or 7 and and then it is prime. Nosotros have tried dividing past all other prime numbers that are less than the square root of 61.

Source: https://www.mathswithmum.com/finding-prime-numbers-to-100/

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