Answer:
The number 4320 is an abundant number.
Multiples of 6 is a perfect number.
Step-by-step explanation:
Given : Number 4320
To find : Is 4320 is perfect, abundant, or deficient?
Solution :
1) A perfect number is one whose factors are equal to a given number i.e. P(n)=n
2) An abundant number is a composite number whose factors, without the number itself, have a sum greater than the number i.e. P(n) >n
3) A deficient number is a composite number in which the sum of its factors is less than the given number i.e. P(n) < n
Number - 4320
Factors are
1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,32,36,40,45,48,54,60,72,80,90,96,108,120,135,144,160,180,216,240,270,288,360,432,480,540,720,864,1080,1440,2160,4320.
If we disregard 4320 as a factor,
Then the sum is
1+2+3+4+5+6+8+9+10+12+15+16+18+20+24+27+30+32+36+40+45+48+54+60+72+80+90+96+108+120+135+144+160+180+216+240+270+288+360+432+480+540+720+864+1080+1440+2160=10800
Now, 10800 >4320
Therefore, The number 4320 is an abundant number.
If we take positive multiples of 6,
Factors of 6, 1,2,3 and 6
The sum of factors except 6,
1+2+3=6
Which means Multiples of 6 is a perfect number.
