What is a prime factorization of a number?
Expressing a given number as a product of factors that are all prime numbers is called the prime factorization of a number.
To write a number as a product of its prime factors, we follow these steps.
Step 1 :
Decompose the given number into prime factors by division method.
Step 2 :
Write all the prime factors as a product. If the same prime factor is repeated, use exponential form to express the factors.
Write the prime factorization of the number:
Problem 1 :
26
Solution :
Decompose 26 into prime factors using division method.
Prime factors of 26 = 2 × 13 |
Problem 2 :
58
Solution :
Decompose 58 into prime factors.
Prime factors of 58 = 2 × 29 |
Problem 3 :
63
Solution :
Decompose 63 into prime factors.
Prime factors of 63 = 3 × 3 × 7 = 32 × 7 |
Problem 4 :
85
Solution :
Decompose 85 into prime factors.
Prime factors of 85 = 5 × 17 |
Problem 5 :
120
Solution :
Decompose 120 into prime factors.
Prime factors of 120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5 |
Problem 6 :
160
Solution :
Decompose 160 into prime factors.
Prime factors of 160 = 2 x 2 x 2 x 2 x 2 x 5 = 25 x 5 |
Problem 7 :
154
Solution :
Decompose 154 into prime factors.
Prime factors of 154 = 2 x 7 x 11 |
Problem 8 :
195
Solution :
Decompose 195 into prime factors.
Prime factors of 195 = 3 x 5 x 13 |
Problem 9 :
225
Solution :
Decompose 225 into prime factors.
Prime factors of 225 = 5 x 5 x 3 x 3 = 52 x 32 |
Problem 10 :
210
Solution :
Decompose 210 into prime factors.
Prime factors of 210 = 2 x 3 x 5 x 7 |
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