# Tag Archives: Multiples

## n-digit number multiple of 2^n, written with 6s’ and 7s’

Find the lowest n-digit number multiple of   ,   written only with   6s’   and   7s’   The first few examples,   n = 1   …     …   6 n = 2 … Continue reading

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## Multiples of 37 and their permutations

A 6-digit number in which the first 3 digits are consecutively-increasing numbers; and the last 3 digits, consecutively-decreasing numbers, is divisible by 37. For example, Can you explain why?                                                                ——————————————   (1) If a 3-digit number of … Continue reading

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## Moving one digit from one end to the other of a number

(period 6) Move 7 :   (period 6) Move 4 :   (period 6) Move 1 :   (period 6) Move 8 :   (period 6) Move 5 :   (period 6) Move 2 :     (period … Continue reading

## Pattern | Sum of all positive integers (multiples of 2 and 5 excluded)

multiples of 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, … multiples of 5 5, 10, 15, 20, 25, 30, …   Let’s take the sum of all positive integers which … Continue reading

## Smallest multiples of N ending in N with sum of digits N (11 ≤ N ≤ 99)

11 ≤ N ≤ 99 To find the smallest multiples of N that ends in N and the sum of digits is N For example, here are the smallest multiples of   13, 17, 19   that satisfy … Continue reading

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## N/k is equal to the sum of the squares of digits of N

Solving the two equations (10*x   +   y)/k   =   x^2   +   y^2 (100*x   +   10*y   +   z)/k   =   x^2   +   y^2   +   z^2 for … Continue reading

## A d-digit num3er multiple of 2^d

For example, d   =   76 2^76   =   75557863725914323419136 A 76-digit number that is a multiple of 2^76 containing only the digits 6 and 7 is: 6667776766677767667676666776766667777767666677766776777777777777666766667776 =   2^76   *   88247290723637794367680048552939376696792027490086866     … Continue reading

## Multiple of 2^d of d-digits containing digits of 2^d

For example, 2^2   =   4 A multiple of 2-digit containing only 4 is 44 2^3   =   8 A multiple of 3-digit containing only 8 is   888 2^5   =   32 A multiple of … Continue reading

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## Multiples of 3-digit num3ers containing one of its digits

Goal:   To find 3-digit numbers such that its consecutive multiples contain one of its digits For example, the number   471   471   *   1   =   471 471   *   2   = … Continue reading

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## 5-digit num3ers divisible by 3-digit contained in the middle of the num3ers

11371                                        11371 / 137  =  83 11398                           … Continue reading