sum of all even divisors of 2^4.3^3 is?
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1200
Step-by-step explanation:
Given :-
2⁴.3³
To find :-
Find the sum of all even divisors ?
Solution :-
Given that :
2⁴.3³
=> (2×2×2×2)×(3×3×3)
=> 16×27
=>432
The factors of 432
=> 1×432
=> 2×216
=> 3×144
=> 4×108
=> 6×72
=> 8×54
=> 9×48
=> 12×36
=> 16×27
=> 18×24
The factors of 432 = 1,2,3,4,6,8,9,12,16,18,24,27,36,54,72,108,144,216,432
Their sum = 1+2+3+4+6+8+9+12+16+18+24+27+36+54+72+108+ 144+216+432 = 1240
now even divisors are 2,4,6,8,12,16,18,24,36,54,72,108,144,216,
432
Their sum = 2+4+6+8+12+16+18+24+36+54+72+108+144+216+432 = 1200
Answer:-
The sum of all even divisors or factors of 2⁴×3³ is 1200
Used formulae:-
- Divisor is also called a Factor.
Points to know :-
- If the number is in the form of N = X^a × Y^b then Sum of factors of N
- = [(X^(a+1)-1)/X-1] × [(Y^(b+1)-1)/Y-1]
where X, Y and Z are the prime numbers and a, b are their respective powers.
- A number A which is divisible by another number B completely then A called a multiple of B and B is the divisor or factor of B.
- If a number is in the form of X^a×Y^b then the number of divisors or factors is (a+1)(b+1)
where X, Y and Z are the prime numbers and a, b are their respective powers.
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