Prime Factorization Chart of Numbers 2-100
The purpose of the chart below is to provide a quick reference of the prime factorization of numbers from 2 to 100. You can use this chart to check your work if you have correctly prime factorized a given number. Think of this as a cheat sheet for the prime factorizations of numbers 2 to 100.
However, if you’re looking for a lesson to learn or refresh your memory regarding the steps on how to find the prime factorization of an integer that is greater than [latex]1[/latex], please check my other lesson on how to perform Prime Factorizations.
Remember though that the number [latex]1[/latex] is neither a prime number nor a composite number. That’s why when somebody asks you what’s the prime factorization of the number [latex]1[/latex], your answer should include the idea that first and foremost [latex]1[/latex] is neither a prime number nor a composite number therefore it doesn’t have one.
On the other hand, if you’re asked to find the prime factorization of a number that you know is prime like the number [latex]13[/latex], your answer should be just the prime number itself which in this case the number [latex]13[/latex].
Numbers 2 to 10
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 2
[latex]2[/latex]
[latex]{2}[/latex]
Number 3
[latex]3[/latex]
[latex]{3}[/latex]
Number 4
[latex]2 \cdot 2[/latex]
[latex]{2^2}[/latex]
Number 5
[latex]5[/latex]
[latex]{5}[/latex]
Number 6
[latex]2 \cdot 3[/latex]
[latex]2 \cdot 3[/latex]
Number 7
[latex]7[/latex]
[latex]7[/latex]
Number 8
[latex]2 \cdot 2 \cdot 2[/latex]
[latex]{2^3}[/latex]
Number 9
[latex]3 \cdot 3[/latex]
[latex]{3^2}[/latex]
Number 10
[latex]2 \cdot 5[/latex]
[latex]2 \cdot 5[/latex]
Numbers 11 to 20
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 11
[latex]11[/latex]
[latex]11[/latex]
Number 12
[latex]2 \cdot 2 \cdot 3[/latex]
[latex]{2^2} \cdot 3[/latex]
Number 13
[latex]13[/latex]
[latex]13[/latex]
Number 14
[latex]2 \cdot 7[/latex]
[latex]2 \cdot 7[/latex]
Number 15
[latex]3 \cdot 5[/latex]
[latex]3 \cdot 5[/latex]
Number 16
[latex]2 \cdot 2 \cdot 2 \cdot 2[/latex]
[latex]{2^4}[/latex]
Number 17
[latex]17[/latex]
[latex]17[/latex]
Number 18
[latex]2 \cdot 3 \cdot 3[/latex]
[latex]2 \cdot {3^2}[/latex]
Number 19
[latex]19[/latex]
[latex]19[/latex]
Number 20
[latex]2 \cdot 2 \cdot 5[/latex]
[latex]{2^2} \cdot 5[/latex]
Numbers 21 to 30
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 21
[latex]3 \cdot 7[/latex]
[latex]3 \cdot 7[/latex]
Number 22
[latex]2 \cdot 11[/latex]
[latex]2 \cdot 11[/latex]
Number 23
[latex]23[/latex]
[latex]23[/latex]
Number 24
[latex]2 \cdot 2 \cdot 2 \cdot 3[/latex]
[latex]{2^3} \cdot 3[/latex]
Number 25
[latex]5 \cdot 5[/latex]
[latex]{5^2}[/latex]
Number 26
[latex]2 \cdot 13[/latex]
[latex]2 \cdot 13[/latex]
Number 27
[latex]3 \cdot 3 \cdot 3[/latex]
[latex]{3^3}[/latex]
Number 28
[latex]2 \cdot 2 \cdot 7[/latex]
[latex]{2^2} \cdot 7[/latex]
Number 29
[latex]29[/latex]
[latex]29[/latex]
Number 30
[latex]2 \cdot 3 \cdot 5[/latex]
[latex]2 \cdot 3 \cdot 5[/latex]
Numbers 31 to 40
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 31
[latex]31[/latex]
[latex]31[/latex]
Number 32
[latex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 2[/latex]
[latex]{2^5}[/latex]
Number 33
[latex]3 \cdot 11[/latex]
[latex]3 \cdot 11[/latex]
Number 34
[latex]2 \cdot 17[/latex]
[latex]2 \cdot 17[/latex]
Number 35
[latex]5 \cdot 7[/latex]
[latex]5 \cdot 7[/latex]
Number 36
[latex]2 \cdot 2 \cdot 3 \cdot 3[/latex]
[latex]{2^2} \cdot {3^2}[/latex]
Number 37
[latex]37[/latex]
[latex]37[/latex]
Number 38
[latex]2 \cdot 19[/latex]
[latex]2 \cdot 19[/latex]
Number 39
[latex]3 \cdot 13[/latex]
[latex]3 \cdot 13[/latex]
Number 40
[latex]2 \cdot 2 \cdot 2 \cdot 5[/latex]
[latex]{2^3} \cdot 5[/latex]
Numbers 41 to 50
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 41
[latex]41[/latex]
[latex]41[/latex]
Number 42
[latex]2 \cdot 3 \cdot 7[/latex]
[latex]2 \cdot 3 \cdot 7[/latex]
Number 43
[latex]43[/latex]
[latex]43[/latex]
Number 44
[latex]2 \cdot 2 \cdot 11[/latex]
[latex]{2^2} \cdot 11[/latex]
Number 45
[latex]3 \cdot 3 \cdot 5[/latex]
[latex]{3^2} \cdot 5[/latex]
Number 46
[latex]2 \cdot 23[/latex]
[latex]2 \cdot 23[/latex]
Number 47
[latex]47[/latex]
[latex]47[/latex]
Number 48
[latex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 3[/latex]
[latex]{2^4} \cdot 3[/latex]
Number 49
[latex]7 \cdot 7[/latex]
[latex]{7^2}[/latex]
Number 50
[latex]2 \cdot 5 \cdot 5[/latex]
[latex]2 \cdot {5^2}[/latex]
Numbers 51 to 60
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 51
[latex]3 \cdot 17[/latex]
[latex]3 \cdot 17[/latex]
Number 52
[latex]2 \cdot 2 \cdot 13[/latex]
[latex]{2^2} \cdot 13[/latex]
Number 53
[latex]53[/latex]
[latex]53[/latex]
Number 54
[latex]2 \cdot 3 \cdot 3 \cdot 3[/latex]
[latex]2 \cdot {3^3}[/latex]
Number 55
[latex]5 \cdot 11[/latex]
[latex]5 \cdot 11[/latex]
Number 56
[latex]2 \cdot 2 \cdot 2 \cdot 7[/latex]
[latex]{2^3} \cdot 7[/latex]
Number 57
[latex]3 \cdot 19[/latex]
[latex]3 \cdot 19[/latex]
Number 58
[latex]2 \cdot 29[/latex]
[latex]2 \cdot 29[/latex]
Number 59
[latex]59[/latex]
[latex]59[/latex]
Number 60
[latex]2 \cdot 2 \cdot 3 \cdot 5[/latex]
[latex]{2^2} \cdot 3 \cdot 5[/latex]
Numbers 61 to 70
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 61
[latex]61[/latex]
[latex]61[/latex]
Number 62
[latex]2 \cdot 31[/latex]
[latex]2 \cdot 31[/latex]
Number 63
[latex]3 \cdot 3 \cdot 7[/latex]
[latex]{3^2} \cdot 7[/latex]
Number 64
[latex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2[/latex]
[latex]{2^6}[/latex]
Number 65
[latex]5 \cdot 13[/latex]
[latex]5 \cdot 13[/latex]
Number 66
[latex]2 \cdot 3 \cdot 11[/latex]
[latex]2 \cdot 3 \cdot 11[/latex]
Number 67
[latex]67[/latex]
[latex]67[/latex]
Number 68
[latex]{2^2} \cdot 17[/latex]
[latex]{2^2} \cdot 17[/latex]
Number 69
[latex]3 \cdot 23[/latex]
[latex]3 \cdot 23[/latex]
Number 70
[latex]2 \cdot 5 \cdot 7[/latex]
[latex]2 \cdot 5 \cdot 7[/latex]
Numbers 71 to 80
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 71
[latex]71[/latex]
[latex]71[/latex]
Number 72
[latex]2 \cdot 2 \cdot 2 \cdot 3 \cdot 3[/latex]
[latex]{2^3} \cdot {3^2}[/latex]
Number 73
[latex]73[/latex]
[latex]73[/latex]
Number 74
[latex]2 \cdot 37[/latex]
[latex]2 \cdot 37[/latex]
Number 75
[latex]3 \cdot 5 \cdot 5[/latex]
[latex]3 \cdot {5^2}[/latex]
Number 76
[latex]2 \cdot 2 \cdot 19[/latex]
[latex]{2^2} \cdot 19[/latex]
Number 77
[latex]7 \cdot 11[/latex]
[latex]7 \cdot 11[/latex]
Number 78
[latex]2 \cdot 3 \cdot 13[/latex]
[latex]2 \cdot 3 \cdot 13[/latex]
Number 79
[latex]79[/latex]
[latex]79[/latex]
Number 80
[latex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 5[/latex]
[latex]{2^4} \cdot 5[/latex]
Numbers 81 to 90
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 81
[latex]3 \cdot 3 \cdot 3 \cdot 3[/latex]
[latex]{3^4}[/latex]
Number 82
[latex]2 \cdot 41[/latex]
[latex]2 \cdot 41[/latex]
Number 83
[latex]83[/latex]
[latex]83[/latex]
Number 84
[latex]2 \cdot 2 \cdot 3 \cdot 7[/latex]
[latex]{2^2} \cdot 3 \cdot 7[/latex]
Number 85
[latex]5 \cdot 17[/latex]
[latex]5 \cdot 17[/latex]
Number 86
[latex]2 \cdot 43[/latex]
[latex]2 \cdot 43[/latex]
Number 87
[latex]3 \cdot 29[/latex]
[latex]3 \cdot 29[/latex]
Number 88
[latex]2 \cdot 2 \cdot 2 \cdot 11[/latex]
[latex]{2^3} \cdot 11[/latex]
Number 89
[latex]89[/latex]
[latex]89[/latex]
Number 90
[latex]2 \cdot 3 \cdot 3 \cdot 5[/latex]
[latex]2 \cdot {3^2} \cdot 5[/latex]
Numbers 91 to 100
NUMBER
PRIME FACTORIZATION
PRIME FACTORIZATION USING EXPONENTS
Number 91
[latex]7 \cdot 13[/latex]
[latex]7 \cdot 13[/latex]
Number 92
[latex]2 \cdot 2 \cdot 23[/latex]
[latex]{2^2} \cdot 23[/latex]
Number 93
[latex]3 \cdot 31[/latex]
[latex]3 \cdot 31[/latex]
Number 94
[latex]2 \cdot 47[/latex]
[latex]2 \cdot 47[/latex]
Number 95
[latex]5 \cdot 19[/latex]
[latex]5 \cdot 19[/latex]
Number 96
[latex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3[/latex]
[latex]{2^5} \cdot 3[/latex]
Number 97
[latex]97[/latex]
[latex]97[/latex]
Number 98
[latex]2 \cdot 7 \cdot 7[/latex]
[latex]2 \cdot 7 \cdot 7[/latex]
Number 99
[latex]3 \cdot 3 \cdot 11[/latex]
[latex]{3^2} \cdot 11[/latex]
Number 100
[latex]2 \cdot 2 \cdot 5 \cdot 5[/latex]
[latex]{2^2} \cdot {5^2}[/latex]