How many of the positive divisors of 120 are also multiples of 4 not

Question

How many of the positive divisors of 120 are also multiples of 4 not including 120?

A. 3.
B. 4.
C. 5.
D. 7.
E. 8.

Nick90 · Accepted Answer

4,8,12,20,24,40,60. (7) is the answer

Other way : factors of 120 = 2^3 * 3*5

Separate 2^2 ( which means 4)

Now, calculate the number of other factors.

2*3*5 = total positive factors are 2*2*2 = 8

This 8 factors include 120

So subtract 1 from 8

Ans is 7

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msk0657 · Answer

Given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120.

Consider factors of 120

4 * 30 
6 * 20
15 * 8
24 * 5 
60 * 2

Total we get 5 different ways and all are part of 4.

IMO C is correct option.

OA please...will correct if I missed anything.

lillianmbula · Answer

I thought it would be 5 as 60, 40, 8, 12 and 20 are all valid

Harish Yannam · Answer

ANSWER IS 6.
 the numbers are 4,12,20,24,40,60.
4 * 30=120. 4 is multiple of 4.
12 * 10=120. 12 is multiple of 4.
20 * 6 =120. 20 is multiple of 4.
24 * 5 =120. 24 is multiple of 4.
40 * 3 =120. 40 is multiple of 4.
60 * 2 =120. 60 is multiple of 4.

Mohdalrabiah92 · Answer

2 * 60 = 120
4 * 30 = 120
8 * 15 = 120
12 * 10 = 120
24 * 5 = 120
20 * 6 = 120
40 * 3 = 120

7 multiples of "4" that also happen to be a positive divisor of 120

Answer D

Bowtye · Answer

There are multiple ways this can be done.

One way of solving is to break 120 down into prime factors:

2^3, 5, 3

How many are also multiples of 4? Remove 2^2 (or 4) from 2^3 to ensure that we get a multiple of 4. Then add up the combinations (this can be done quicker than listing them out but I will list out here)

1. 2^2
2. 2^2 *2
3. 2^2*3
4. 2^2 *5
5. 2^2*2*3
6. 2^2*2*5
7. 2^2*3*5

note that 2^2*3*5*2 does not count because that is equal to 120

forgot to put answer

D: 7

Harish Yannam · Answer

2 isnt multiple of 4. 4 is a multiple of 2.

Nick90 · Answer

Similarly in above question, if we are asked to calculate the multiples of 3

Factors of 120 =. 2^3*3*5

Separate 3

Now, 2^3 * 5

Total factors = 4*2

= 8

Subtract 1 if you dont want to include 120

Other way. : 3,6,12,15,24,30,60
(120 not included as per question)

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Mohdalrabiah92 · Answer

4, 8, 12, 20, 24, 40, 60

Divyadisha · Answer

factors of 120 = 2*2*2*3*5

In order to have 4 we need 2*2
So we have below multiples except 120
2*2
2*2*2
2*2*3
2*2*2*3
2*2*5
2*2*2*5
2*2*3*5

Total 7 factors.
D is the answer

nikhilbansal08 · Answer

1 *120
2 *60
3 * 40
4 *30
5 *24
6 *20
8 *15
10* 12

required multiples for 4 are : 60, 40 ,4, 20,24,8,12.... so D is the answer.

Nightfury14 · Answer

120 factors are 2*2*2*3*5

Multiples of 4 not including 120
   2*2   = 4
  2*2  *2 = 8
  2*2  *3 = 12
  2*2  *5 = 20
  2*2  *2*3 = 24
  2*2  *2*5 = 40
  2*2  *3*5 = 60

Total 7 Answer (D)

ScottTargetTestPrep · Answer

120 = 4 x 30

The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

So taking away the factor 30 (since 4 x 30 = 120), there are 7 divisors of 120 (not including 120) that are multiples of 4.

Answer: D

Kinshook · Answer

Asked: How many of the positive divisors of 120 are also multiples of 4 not including 120?

120 = 2^3*3*5

Divisors of 120 are also multiples of 4  = 2^2 (2^{0-1}3^{0-1}5^{0-1})  = 2*2*2 = 8
positive divisors of 120 are also multiples of 4 not including 120 = 8-1 =7

IMO D

KarishmaB · Answer

Prime factorise 120 = 2^3 * 3 * 5 For the factor to be a multiple of 4, we must have at least two 2s. All other prime factors are optional. So we can pick 2s in 2 ways (either 2 2s or 3 2s) We can pick a 3 in 2 ways (either 0 3s or 1 3) We can pick a 5 in 2 ways (either 0 5s or 1 5) Total number of factors = 2*2*2 = 8 but this will include 120 too (when all factors are picked) So total acceptable factors = 7 Answer (D) For more details, check: https://anaprep.com/number-properties-f ... -a-number/

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How many of the positive divisors of 120 are also multiples of 4 not

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