Study guides

☆☆

Q: Is the number 32 an abundant deficient or perfect number?

Write your answer...

Submit

Still have questions?

Related questions

no

Deficient. The sum of its proper factors is 1+2+4+8+16+32+64+128+256+512 = 1023. Since that sum is less than 1024, it is deficient.

32 is not Perfect.

Deficient number From Wikipedia, the free encyclopediaIn mathematics, a deficient number or defective number is a number n for which Ïƒ(n) < 2n. Here Ïƒ(n) is the sum-of-divisors function: the sum of all positive divisors of n, including nitself. An equivalent definition is that the sum of all proper divisors of the number (divisors other than the number itself) is less than the number. The value 2n âˆ’ Ïƒ(n) is called the deficiency of n.The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, â€¦ (sequence A005100 in OEIS)As an example, consider the number 21. Its divisors are 1, 3, 7 and 21, and their sum is 32. Because 32 is less than 2 Ã— 21, the number 21 is deficient. Its deficiency is 2 Ã— 21 âˆ’ 32 = 10.An infinite number of both even and odd deficient numbers exist. For example, all odd numbers with one or two distinct prime factors, and all proper divisors of deficient or perfect numbers are deficient.Closely related to deficient numbers are perfect numbers with Ïƒ(n) = 2n, and abundant numbers with Ïƒ(n) > 2n. The natural numbers were first classified as either deficient, perfect or abundant byNicomachus in his Introductio Arithmetica (circa 100).

32+16+8+4+2+1=63. 64 is deficient.

2: 1, 2 (3) deficient 3: 1, 3 (4) deficient 4: 1, 2, 4 (7) deficient 5: 1, 5 (6) deficient 6: 1, 2, 3, 6 (12) perfect 7: 1, 7 (8) deficient 8: 1, 2, 4, 8 (15) deficient 9: 1, 3, 9 (13) deficient 10: 1, 2, 5, 10 (18) deficient 11: 1, 11 (12) deficient 12: 1, 2, 3, 4, 6, 12 (28) abundant 13: 1, 13 (14) deficient 14: 1, 2, 7, 14 (24) deficient 15: 1, 3, 5, 15 (24) deficient 16: 1, 2, 4, 8, 16 (31) deficient 17: 1, 17 (18) deficient 18: 1, 2, 3, 6, 9, 18 (39) abundant 19: 1, 19 (20) deficient 20: 1, 2, 4, 5, 10, 20 (42) abundant 21: 1, 3, 7, 21 (32) deficient 22: 1, 2, 11, 22 (26) deficient 23: 1, 23 (24) deficient 24: 1, 2, 3, 4, 6, 8, 12, 24 (60) abundant 25: 1, 5, 25 (31) deficient 26: 1, 2, 13, 26 (42) deficient 27: 1, 3, 9, 27 (40) deficient 28: 1, 2, 4, 7, 14, 28 (56) perfect 29: 1, 29 (30) deficient 30: 1, 2, 3, 5, 6, 10, 15, 30 (72) abundant

No.

How about: 32*32 = 1024

No. The proper divisors of 32 are 1, 2, 4, 8, and 16. Their sum, 1 + 2 + 4 + 8 + 16 = 31, which is less than 32, so it is not an abundant number.

No, because 32 is not a perfect square.

16 2*16 = 32

No, 32 is a perfect square of nine and it is 4th Motzkin number.

People also asked