5. Write each of the following as a product
of its prime factors.
a) 27 (b) 36 fc) 52 id} 63
fe) 72 ft) 100 lg) 126 tm 150
W 180 (j) 225 ;k) 240 fj) 360
a) 27 = 3 * 3 * 3
b) 36 = 2 * 2 * 3 * 3
c) 52 = 2 * 2 * 13
d) 63 = 3 * 3 * 7
e) 72 = 2 * 2 * 2 * 3 * 3
f) 100 = 2 * 2 * 5 * 5
g) 126 = 2 * 3 * 3 * 7
h) 150 = 2 * 3 * 5 * 5
i) 180 = 2 * 2 * 3 * 3 * 5
j) 225 = 3 * 3 * 5 * 5
k) 240 = 2 * 2 * 2 * 2 * 3 * 5
l) 360 = 2 * 2 * 2 * 3 * 3 * 5
a) To write 27 as a product of its prime factors, we can start by finding the prime factorization of 27.
27 can be expressed as 3 * 3 * 3.
So, the product of the prime factors of 27 is 3^3.
b) To write 36 as a product of its prime factors, we can start by finding the prime factorization of 36.
36 can be expressed as 2 * 2 * 3 * 3.
So, the product of the prime factors of 36 is 2^2 * 3^2.
c) To write 52 as a product of its prime factors, we can start by finding the prime factorization of 52.
52 can be expressed as 2 * 2 * 13.
So, the product of the prime factors of 52 is 2^2 * 13.
d) To write 63 as a product of its prime factors, we can start by finding the prime factorization of 63.
63 can be expressed as 3 * 3 * 7.
So, the product of the prime factors of 63 is 3^2 * 7.
e) To write 72 as a product of its prime factors, we can start by finding the prime factorization of 72.
72 can be expressed as 2 * 2 * 2 * 3 * 3.
So, the product of the prime factors of 72 is 2^3 * 3^2.
f) To write 100 as a product of its prime factors, we can start by finding the prime factorization of 100.
100 can be expressed as 2 * 2 * 5 * 5.
So, the product of the prime factors of 100 is 2^2 * 5^2.
g) To write 126 as a product of its prime factors, we can start by finding the prime factorization of 126.
126 can be expressed as 2 * 3 * 3 * 7.
So, the product of the prime factors of 126 is 2 * 3^2 * 7.
h) To write 150 as a product of its prime factors, we can start by finding the prime factorization of 150.
150 can be expressed as 2 * 3 * 5 * 5.
So, the product of the prime factors of 150 is 2 * 3 * 5^2.
i) To write 180 as a product of its prime factors, we can start by finding the prime factorization of 180.
180 can be expressed as 2 * 2 * 3 * 3 * 5.
So, the product of the prime factors of 180 is 2^2 * 3^2 * 5.
j) To write 225 as a product of its prime factors, we can start by finding the prime factorization of 225.
225 can be expressed as 3 * 3 * 5 * 5.
So, the product of the prime factors of 225 is 3^2 * 5^2.
k) To write 240 as a product of its prime factors, we can start by finding the prime factorization of 240.
240 can be expressed as 2 * 2 * 2 * 2 * 3 * 5.
So, the product of the prime factors of 240 is 2^4 * 3 * 5.
l) To write 360 as a product of its prime factors, we can start by finding the prime factorization of 360.
360 can be expressed as 2 * 2 * 2 * 3 * 3 * 5.
So, the product of the prime factors of 360 is 2^3 * 3^2 * 5.
To write each of the given numbers as a product of its prime factors, you need to find the prime numbers that can divide the given number evenly.
a) 27:
The prime factors of 27 are 3 and 3, because 3 × 3 = 9 and 9 × 3 = 27. So, the prime factorization of 27 is 3 × 3 × 3 or 3^3.
b) 36:
The prime factors of 36 are 2, 2, 3, and 3, because 2 × 2 × 3 × 3 = 36. So, the prime factorization of 36 is 2^2 × 3^2.
c) 52:
The prime factors of 52 are 2, 2, 13, because 2 × 2 × 13 = 52. So, the prime factorization of 52 is 2^2 × 13.
d) 63:
The prime factors of 63 are 3, 3, 7, because 3 × 3 × 7 = 63. So, the prime factorization of 63 is 3^2 × 7.
e) 72:
The prime factors of 72 are 2, 2, 2, 3, 3, because 2 × 2 × 2 × 3 × 3 = 72. So, the prime factorization of 72 is 2^3 × 3^2.
f) 100:
The prime factors of 100 are 2, 2, 5, 5, because 2 × 2 × 5 × 5 = 100. So, the prime factorization of 100 is 2^2 × 5^2.
g) 126:
The prime factors of 126 are 2, 3, 3, 7, because 2 × 3 × 3 × 7 = 126. So, the prime factorization of 126 is 2^1 × 3^2 × 7^1.
h) 150:
The prime factors of 150 are 2, 3, 5, 5, because 2 × 3 × 5 × 5 = 150. So, the prime factorization of 150 is 2^1 × 3^1 × 5^2.
i) 180:
The prime factors of 180 are 2, 2, 3, 3, 5, because 2 × 2 × 3 × 3 × 5 = 180. So, the prime factorization of 180 is 2^2 × 3^2 × 5^1.
j) 225:
The prime factors of 225 are 3, 3, 5, 5, because 3 × 3 × 5 × 5 = 225. So, the prime factorization of 225 is 3^2 × 5^2.
k) 240:
The prime factors of 240 are 2, 2, 2, 2, 3, 5, because 2 × 2 × 2 × 2 × 3 × 5 = 240. So, the prime factorization of 240 is 2^4 × 3^1 × 5^1.
l) 360:
The prime factors of 360 are 2, 2, 2, 3, 3, 5, because 2 × 2 × 2 × 3 × 3 × 5 = 360. So, the prime factorization of 360 is 2^3 × 3^2 × 5^1.
Now, you can write each of the given numbers as a product of its prime factors by following the steps above.