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Counting numbers whose GCD (HCF) with a given number is a given value

This type of question, asked 4 times: 2021 Paper 26, 14 Jun 2022, 26 Jun 2022, 29 Jan 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 26

    81
    The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is

  2. Question 2

    14 Jun 2022

    174
    The sum of all the elements of the set {α∈{1,2,…,100}:HCF(α,24)=1}\mathbf{\{}\alpha\mathbf{\in \{ 1,2,\ldots,100\}:HCF(}\alpha,24) = 1\} is

  3. Question 3

    26 Jun 2022

    174
    The total number of 3-digit numbers, whose greatest common divisor with 36 is 2 , is

  4. Question 4

    29 Jan 2023

    171
    The total number of 4 -digit numbers whose greatest common divisor with 54 is 2 , is