How can you find the total number of factors of any number
Answers
Answer:
by prime factorisation.
Answer:
If we have to find the number of factors of any number say N, then we should follow below steps:
Step 1: Prime factorize
N
=
p
a
×
q
b
×
r
c
×
…
Step 2: The number of factors of N= (a+1)(b+1)(c+1)…
Sum of factors
To find the sum of all the factors of a number (say N), we follow below two steps:
Step 1: Prime factorize
N
=
p
a
×
q
b
×
r
c
×
…
Step 2: Sum of factors =
(
p
a
+
1
–
1
p
–
1
)
(
q
b
+
1
–
1
q
–
1
)
(
r
c
+
1
–
1
r
–
1
)
…
Product of Factors
To find the product of all the factors of a number (say N), we follow below three steps:
Step 1: Prime factorize
N
=
p
a
×
q
b
×
r
c
×
…
Step 2: Let the number of factors of N be x. therefore, x= (a+1)(b+1)(c+1)…
Step 3: Product of factors =
N
x
2
Let us take an example to understand the working of the above formulas.
Question: Find the number of factors, the sum of factors and product of factors of 1800.
Solution:
Prime factorization of
1800
=
2
3
×
3
2
×
5
2
Number of factors 1800= (3+1)(2+1)(2+1) = 36
Sum of factors of 1800
=
(
2
3
+
1
–
1
2
–
1
)
(
3
2
+
1
–
1
3
–
1
)
(
5
2
+
1
–
1
5
–
1
)
=
15
×
4
×
31
=
1860
Product of Factors of 1800=
1800
36
2
=
1800
18
Step-by-step explanation:
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