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kinshuk97gupta
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What is the number of common factors between 75 and 300? 29 Jul 2020, 09:12
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Difficulty:

45% (medium)

Question Stats:

62% (01:20) correct 38% (01:16) wrong based on 454 sessions

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What is the number of common factors between 75 and 300?

A) 2
B) 3
C) 5
D) 6
E) 18
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Official Answer
D
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What is the number of common factors between 75 and 300? 29 Jul 2020, 10:21
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kinshuk97gupta
What is the number of common factors between 75 and 300?

A) 2
B) 3
C) 5
D) 6
E) 18
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Factors of 75 - 1,3,5,15,25,75
Since 75 is also a factor of 300, all the factors of 75 would be common factors.

Ans: 6
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What is the number of common factors between 75 and 300? 29 Jul 2020, 10:25
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Solution


Given

To Find

    • The number of common factors between 75 and 300.

Approach and Working Out

    • 75 = 3 × \(5^2\) and 300 =\( 2^2\) × 3 × \(5^2\)
      o GCD of 75 and 300 = 3 × \(5^2\)
    • Number of factors of 3 × \(5^2\),
      =2 × 3
      =6


Correct Answer: Option D
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What is the number of common factors between 75 and 300? 30 Jul 2020, 11:02
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kinshuk97gupta
What is the number of common factors between 75 and 300?

A) 2
B) 3
C) 5
D) 6
E) 18
Show more


Just a Note:

When I first read the question I interpreted " between 75 and 300" to mean all the numbers from 76 to 299, i.e 76,77,78,79......297,298,299. In this interpretation, the question made no sense.

Apparently that is not the case and the question means number of common factors of 75 and 300. Perhaps the question could have been better framed to avoid this ambiguity.
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What is the number of common factors between 75 and 300? 01 Jul 2023, 10:36
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EgmatQuantExpert

Solution


Given

To Find

    • The number of common factors between 75 and 300.

Approach and Working Out

    • 75 = 3 × \(5^2\) and 300 =\( 2^2\) × 3 × \(5^2\)
      o GCD of 75 and 300 = 3 × \(5^2\)
    • Number of factors of 3 × \(5^2\),
      =2 × 3
      =6


Correct Answer: Option D
Show more


Bunuel I have a question. Can you please clarify? Is the number of factors above based on the following fact?

75 can only have odd factors. Now since GCD of 75 and 300 = \(3^1\) × \(5^2\), the total number of odd factors is (1+1)*(2+1) = 6. Therefore, the total # common factors of 75 and 300 is 6. Is this correct understanding? Thanks!
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What is the number of common factors between 75 and 300? 01 Jul 2023, 11:13
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Engineer1
What is the number of common factors between 75 and 300?

A) 2
B) 3
C) 5
D) 6
E) 18

EgmatQuantExpert

Solution


Given

To Find

    • The number of common factors between 75 and 300.

Approach and Working Out

    • 75 = 3 × \(5^2\) and 300 =\( 2^2\) × 3 × \(5^2\)
      o GCD of 75 and 300 = 3 × \(5^2\)
    • Number of factors of 3 × \(5^2\),
      =2 × 3
      =6


Correct Answer: Option D


Bunuel I have a question. Can you please clarify? Is the number of factors above based on the following fact?

75 can only have odd factors. Now since GCD of 75 and 300 = \(3^1\) × \(5^2\), the total number of odd factors is (1+1)*(2+1) = 6. Therefore, the total # common factors of 75 and 300 is 6. Is this correct understanding? Thanks!
Show more

A simpler approach would be as follows. Since 75 itself is a factor of 300, all positive factors of 75 will automatically be factors of 300. Therefore, the number of common positive factors of 75 and 300 will correspond to the number of factors of 75. The number of factors of 75 = 3*5^2 is (1 + 1)(2 + 1) = 6.

Answer: D.
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What is the number of common factors between 75 and 300? 25 Oct 2024, 10:55
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