Saturday, 23 March 2019
Find the number of zeroes at the end of 48!.
Find the number of zeroes at the end of 48!.
Solution:
Maximum power of 5 in 48!
= 9 + 1
= 10
This way:
[ 48 / 5 ] + [48/5x5] + [48 / 5x5x5] + …….. [till the quotient is greater than zero]
= 9 + 1 + 0
= 10
Answer: 10
Thursday, 14 March 2019
Friday, 8 March 2019
What is the total number of divisors of 1728?
Find the number of divisors of 1728
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Exponents: 6 & 3
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Solution:
Prime
Factorization of 1728:
2 | 1728
2 | 864
2 | 864
2 | 432
2 | 216
2 | 108
2 | 54
3 | 27
3 | 9
3 | 3
| 1
2^6, 3^3 Exponents: 6 & 3
Add 1 to each exponent (6+1) (3+1)
Multiple “exponents+1” together = (6+1) x (3+1) =7 x 4 = 28
Multiple “exponents+1” together = (6+1) x (3+1) =7 x 4 = 28
Total number of divisors
of 1728 = 28
What is the total number of divisors of 600?
Numbers: Find the number of divisors of 600
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Example:
Find the number of divisors of 600
Solution:
Prime Factorization of 600:
2 | 600
2 | 300
2 | 150
3 | 75
5 | 25
5 | 5
| 1
2^3, 3^1 & 5^2
Exponents: 3, 1 & 2
Add 1 to each exponent = (3+1) (1+1) (2+1)
Multiple “exponents+1” together = (3+1) x (1+1) x (2+1) = 4 x 2 x 3 = 24
Total number of divisors of 600 = 24
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Example:
Find the number of divisors of 600
Solution:
Prime Factorization of 600:
2 | 600
2 | 300
2 | 150
3 | 75
5 | 25
5 | 5
| 1
2^3, 3^1 & 5^2
Exponents: 3, 1 & 2
Add 1 to each exponent = (3+1) (1+1) (2+1)
Multiple “exponents+1” together = (3+1) x (1+1) x (2+1) = 4 x 2 x 3 = 24
Total number of divisors of 600 = 24
Find the sum of divisors of 544
Find the sum of divisors of 544.
Method:
Find the the prime factorization of the number
Calculate the sum of its divisors
Take each different prime factor
Add together all its powers up to the one that appears in the prime factorization
And then multiply all these sums together!
Method:
Find the the prime factorization of the number
Calculate the sum of its divisors
Take each different prime factor
Add together all its powers up to the one that appears in the prime factorization
And then multiply all these sums together!
Solution:
Prime
Factorization of 544:
2 | 544
2 | 272
2 | 136
2 | 68
2 | 34
17 | 17
17 | 17
| 1
2^5 x 17^1
Exponents: 5 & 1
Sum of divisors of 544 = 1134
2^5 x 17^1
Exponents: 5 & 1
X
|
2^0
|
2^1
|
2^2
|
2^3
|
2^4
|
2^5
|
Row Sum
|
17^0
|
1
|
2
|
4
|
8
|
16
|
32
|
63
|
17^1
|
17
|
34
|
68
|
136
|
272
|
544
|
1071
|
Col Sum
|
18
|
36
|
72
|
144
|
288
|
576
|
1134
|
Sum of divisors of 544 = 1134
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