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15 Jun 2026, 13:58
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:32) correct
46%
(02:22)
wrong
based on 81
sessions
History
Date
Time
Result
Not Attempted Yet
The sum of the positive divisors of 45 is 78. What is the sum of all positive divisors of 720?
A. 1,248
B. 2,184
C. 2,418
D. 2,808
E. 3,120
A. 1,248
B. 2,184
C. 2,418
D. 2,808
E. 3,120
ankushsambare
Joined: 13 Jun 2022
Last visit: 06 Sep 2026
Posts: 313
Given Kudos: 230
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
Products:
15 Jun 2026, 19:48
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720 = 2^4 × 3^2 × 5
Sum of divisors formula:
(1 + 2 + 2^2 + 2^3 + 2^4)(1 + 3 + 3^2)(1 + 5)
= (1 + 2 + 4 + 8 + 16)(1 + 3 + 9)(1 + 5)
= 31 × 13 × 6
= 403 × 6
= 2418
Answer: 2418
GMAT shortcut:
For n = p^a × q^b × r^c,
Sum of divisors = [(p^(a+1) − 1)/(p − 1)] × [(q^(b+1) − 1)/(q − 1)] × [(r^(c+1) − 1)/(r − 1)]
So,
= (2^5 − 1)/(2 − 1) × (3^3 − 1)/(3 − 1) × (5^2 − 1)/(5 − 1)
= 31 × 13 × 6
= 2418
Answer: C (2418)
Sum of divisors formula:
(1 + 2 + 2^2 + 2^3 + 2^4)(1 + 3 + 3^2)(1 + 5)
= (1 + 2 + 4 + 8 + 16)(1 + 3 + 9)(1 + 5)
= 31 × 13 × 6
= 403 × 6
= 2418
Answer: 2418
GMAT shortcut:
For n = p^a × q^b × r^c,
Sum of divisors = [(p^(a+1) − 1)/(p − 1)] × [(q^(b+1) − 1)/(q − 1)] × [(r^(c+1) − 1)/(r − 1)]
So,
= (2^5 − 1)/(2 − 1) × (3^3 − 1)/(3 − 1) × (5^2 − 1)/(5 − 1)
= 31 × 13 × 6
= 2418
Answer: C (2418)
17 Jun 2026, 02:33
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What if you didn’t know that formula
