The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:
Answers
Answered by
110
Solution:-
(3 × 5)^12 × (2 × 7)^10 × (10)^25
= (3)¹² × (5)¹² × (2)¹⁰ × (7)¹⁰ × (2)²⁵ × (5)²⁵
= (3)¹² × (5)¹²⁺²⁵ × (2)¹⁰⁺²⁵ × (7)¹⁰
= (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰
Now, it cannot be further factorised hence this is the prime factorisation of the above number.
So, (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰ has total
12 + 37 + 35 + 10 = 94 prime factors.
Answer.
(3 × 5)^12 × (2 × 7)^10 × (10)^25
= (3)¹² × (5)¹² × (2)¹⁰ × (7)¹⁰ × (2)²⁵ × (5)²⁵
= (3)¹² × (5)¹²⁺²⁵ × (2)¹⁰⁺²⁵ × (7)¹⁰
= (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰
Now, it cannot be further factorised hence this is the prime factorisation of the above number.
So, (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰ has total
12 + 37 + 35 + 10 = 94 prime factors.
Answer.
Answered by
8
Answer:
94 prime factors
Step-by-step explanation:
the above equation can be also written as
3^12*5^37*2^35*7^10
=12+37+35+10=94
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