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Quant · Number System

Number System

10 sub-topics · 84 lessons · 98 questions · 45 PYQs

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Divisibility Rules10 lessons · 17 questions · 9 PYQs

What this sub-topic covers

Factors and Divisors10 lessons · 11 questions · 8 PYQs

What this sub-topic covers

Remainders12 lessons · 10 questions · 5 PYQs

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Unit and Last Digits7 lessons · 5 questions · 2 PYQs

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Factorials and Trailing Zeros6 lessons · 5 questions · 1 PYQs

What this sub-topic covers

Digits and Number Forms8 lessons · 16 questions · 3 PYQs

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Integer Solutions of Equations8 lessons · 9 questions · 6 PYQs

What this sub-topic covers

Types of Numbers7 lessons · 12 questions · 3 PYQs

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Simplification and Approximation9 lessons · 10 questions · 8 PYQs

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Number Bases7 lessons · 3 questions

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Formula sheet

Division algorithm
$N=dq+r,\quad 0\le r<d$
Three-digit reversal difference
$\overline{abc}-\overline{cba}=99(a-c)$
Chained division
$A\div B\div C=\frac{A}{BC}\ne\frac{AC}{B}$
Solving for an unknown base
$(ab)_x=N\ \Rightarrow\ ax+b=N,\ x>\max(a,b)$
Number of divisors
$N=\prod p_i^{e_i}\ \Rightarrow\ d(N)=\prod(e_i+1)$
Co-prime factor pairs
$\#\{N=xy,\ \gcd(x,y)=1,\ x\le y\}=2^{\omega(N)-1}$
Place value in base b
$(d_k\dots d_1d_0)_b=\sum d_i b^{i},\quad 0\le d_i<b$
Always-divisible power differences
$a\equiv1\pmod m\Rightarrow m\mid a^{n}-1\ \forall n$