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A Number That Can Only Be Divided by One and Itself

Written By Tuesday, February 15, 2022 Add Comment Edit

Prime numbers and divisibility

Lesson 1.

A prime number is a whole number greater than 1 that can only be divided by itself and 1. The smallest prime number numbers are 2, 3, 5, 7, eleven, 13, 17, xix and 23.  The number 2 is the only even prime number.

Example:

7=1�7  The number 7 has but two factors: 1 and itself.
eleven=ane �xi  The number xi has only two factors: one and itself.

Composite numbers:   A blended number has more than 2 factors. Blended numbers tin can be broken downward into prime factors.

Example:

6 = ii �3  two and 3 are prime numbers.
20 = 2 �2�5  2 and v are prime numbers.
35 = 5 �seven  v and 7 are prime numbers.

Prime number factors:    Find the prime factors of 30.

30 = 2 �3�5

The prime factors of thirty are the numbers two, 3,  and 5.

  • Begin with the lowest prime number that is a gene of 30. Dissever by ii to get the cistron 15.
  • Now apply the lowest prime number that is a factor of 15. Split by three to get the factor five which is as well a prime number.
You can besides discover the prime factors of a whole number by drawing a factor tree.
30 = 2 �3�v

Divisibility of numbers:
You can use the Sieve of Eratosthenes to detect prime numbers.

2 3 4 v half dozen 7
8 9 x 11 12 thirteen
fourteen fifteen 16 17 xviii 19
xx 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 forty 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
eighty 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
two three iv 5 vi 7
8 nine ten 11 12 xiii
fourteen 15 16 17 18 xix
twenty 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
80 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
All even numbers are divisble past 2. If the sum of the digits of the number tin be divided by 3 , the number is divisible by 3 .
2 3 four five 6 7
8 9 10 11 12 13
14 15 xvi 17 18 19
20 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
80 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
2 3 4 v 6 7
8 9 10 11 12 13
14 15 16 17 18 19
20 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
eighty 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
If the last 2 digits of a number tin be divided past 4, the number is divisible by iv.

Case: one 12 � four = 28 and 12 � four = 3

If a number ends in 0 or five, it is divisible by 5.
2 3 4 v six 7
8 9 10 11 12 xiii
14 15 16 17 18 19
20 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 xl 41 42 43
44 45 46 47 48 49
fifty 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 seventy 71 72 73
74 75 76 77 78 79
80 81 82 83 84 85
86 87 88 89 ninety 91
92 93 94 95 96 97
98 99 100 101 102 103
2 three iv 5 vi 7
8 9 x eleven 12 13
14 15 16 17 18 19
twenty 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 threescore 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
fourscore 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
If a number can be divided by two and 3, it is divisible by 6. These numbers are divisible by 7.
2 iii 4 5 6 7
viii 9 10 11 12 xiii
fourteen fifteen 16 17 18 19
20 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
fifty 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
lxxx 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
2 iii 4 five 6 vii
eight nine 10 eleven 12 13
14 xv 16 17 18 nineteen
twenty 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
80 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
These numbers are divisible past 8. If the sum of the digits of the number can be divided by 9 , the number is divisible by nine .

Case: 54 � ix = half dozen 5 + 4 = 9

The first 27 prime numbers are shown hither in yellow in the table below.

2 3 4 5 vi seven
8 9 x 11 12 13
fourteen fifteen 16 17 xviii 19
20 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72 73
74 75 76 77 78 79
80 81 82 83 84 85
86 87 88 89 ninety 91
92 93 94 95 96 97
98 99 100 101 102 103
two 3 4 5 6 7
8 9 ten 11 12 13
14 fifteen 16 17 18 19
twenty 21 22 23 24 25
26 27 28 29 30 31
32 33 34 35 36 37
38 39 40 41 42 43
44 45 46 47 48 49
50 51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 seventy 71 72 73
74 75 76 77 78 79
fourscore 81 82 83 84 85
86 87 88 89 90 91
92 93 94 95 96 97
98 99 100 101 102 103
Y'all can find these prime numbers past crossing out the multiples of two, 3, v and 7 (except for themselves) on the chart.

Practice these methods and and then take Quiz ane on Prime numbers.
Ps. Retrieve to utilise the checklist to keep track of your work.

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Source: http://www.rasmus.is/uk/t/u/st23k01.HTM

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