What is smallest number by which 625 must be divided so that the quotient is a perfect cube a 125 b 5 c 2 D 3?

DownloadApp

Home » Aptitude » Simplification » Question

1. What is the smallest number by which 625 must be divided so that the quotient is a perfect cube ?

∴  625 = 5 × 5 × 5 × 5 = 53 × 5For the smallest cube number,625 should be divided 5,

625 ÷ 5 = 125 = 53

(i) We have,

1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

After grouping the prime factors in triplets, it’s seen that one factor 3 is left without grouping.

1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3

So, in order to make it a perfect cube, it must be divided by 3.

Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3.

(ii) We have,

10985 = 5 × 13 × 13 × 13

After grouping the prime factors in triplet, it’s seen that one factor 5 is left without grouping.

10985 = 5 × (13 × 13 × 13)

So, it must be divided by 5 in order to get a perfect cube.

Thus, the required smallest number is 5.

(iii) We have,

28672 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7

After grouping the prime factors in triplets, it’s seen that one factor 7 is left without grouping.

28672 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 7

So, it must be divided by 7 in order to get a perfect cube.

Thus, the required smallest number is 7.

(iv) 13718 = 2 × 19 × 19 × 19

After grouping the prime factors in triplets, it’s seen that one factor 2 is left without grouping.

13718 = 2 × (19 × 19 × 19)

So, it must be divided by 2 in order to get a perfect cube.

Thus, the required smallest number is 2.

Math Expert

Joined: 02 Sep 2009

Posts: 86880

What is the smallest positive integer by which 625 must be divided so [#permalink]

  26 Aug 2022, 20:30

00:00

Difficulty:

15% (low)

Question Stats:

82% (00:49) correct 18% (00:53) wrong based on 38 sessions

Hide Show timer Statistics

What is the smallest positive integer by which 625 must be divided so that the quotient is a perfect cube?(A) 125 (B) 25(C) 5(D) 3

(E) 2

_________________

Intern

Joined: 25 Nov 2021

Posts: 4

Location: India

Re: What is the smallest positive integer by which 625 must be divided so [#permalink]

  30 Aug 2022, 04:48

Option: CPrime factorization of 625 is625 = 5 × 5 × 5 × 5As seen above the smallest prime factor is 5Here a perfect cube would be 5 x 5 x 5 = 125Therefore 5 is the smallest positive integer by which 625 must be divided to get a perfect cube as a quotient.

Posted from my mobile device

Re: What is the smallest positive integer by which 625 must be divided so [#permalink]

30 Aug 2022, 04:48

Correct Answer:

Description for Correct answer:

5 | 625 5 | 125 5 | 25 5 | 5 | 1\( \Large 625 = 5 \times 5 \times 5 \times 5 \)

Smallest number = 5

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

Comments

Similar Questions