Cohart

Episode 7 — DSA with JavaScript / 7.7 — Math Problems and Algorithms

7.7 — Quick Revision: Math Problems

<< Overview

Key formulas

Operation	Formula/Method	Time
GCD	Euclidean algorithm	O(log min)
LCM	a*b/gcd(a,b)	O(log min)
Prime check	Test 2..√n	O(√n)
Sieve	Mark composites	O(n log log n)
Fast power	Square & multiply	O(log n)
nCr	Incremental multiply	O(r)
Factorial	Loop 1..n	O(n)
Trailing zeros n!	Count 5s	O(log n)

Common number properties

Armstrong: digit^k sum = number
Palindrome: reverse equals original
Perfect: sum of proper divisors = number
Harshad: divisible by digit sum

Self-check drill

SC-001

Q: GCD of 48 and 18?
A: 6

SC-002

Q: Is 29 prime?
A: Yes

SC-003

Q: Trailing zeros in 100!?
A: 24

SC-004

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-005

Q: LCM(4,6)?
A: 12

SC-006

Q: Fast power complexity?
A: O(log n)

SC-007

Q: Sieve complexity?
A: O(n log log n)

SC-008

Q: nCr(5,2)?
A: 10

SC-009

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-010

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-011

Q: GCD of 48 and 18?
A: 6

SC-012

Q: Is 29 prime?
A: Yes

SC-013

Q: Trailing zeros in 100!?
A: 24

SC-014

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-015

Q: LCM(4,6)?
A: 12

SC-016

Q: Fast power complexity?
A: O(log n)

SC-017

Q: Sieve complexity?
A: O(n log log n)

SC-018

Q: nCr(5,2)?
A: 10

SC-019

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-020

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-021

Q: GCD of 48 and 18?
A: 6

SC-022

Q: Is 29 prime?
A: Yes

SC-023

Q: Trailing zeros in 100!?
A: 24

SC-024

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-025

Q: LCM(4,6)?
A: 12

SC-026

Q: Fast power complexity?
A: O(log n)

SC-027

Q: Sieve complexity?
A: O(n log log n)

SC-028

Q: nCr(5,2)?
A: 10

SC-029

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-030

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-031

Q: GCD of 48 and 18?
A: 6

SC-032

Q: Is 29 prime?
A: Yes

SC-033

Q: Trailing zeros in 100!?
A: 24

SC-034

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-035

Q: LCM(4,6)?
A: 12

SC-036

Q: Fast power complexity?
A: O(log n)

SC-037

Q: Sieve complexity?
A: O(n log log n)

SC-038

Q: nCr(5,2)?
A: 10

SC-039

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-040

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-041

Q: GCD of 48 and 18?
A: 6

SC-042

Q: Is 29 prime?
A: Yes

SC-043

Q: Trailing zeros in 100!?
A: 24

SC-044

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-045

Q: LCM(4,6)?
A: 12

SC-046

Q: Fast power complexity?
A: O(log n)

SC-047

Q: Sieve complexity?
A: O(n log log n)

SC-048

Q: nCr(5,2)?
A: 10

SC-049

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-050

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-051

Q: GCD of 48 and 18?
A: 6

SC-052

Q: Is 29 prime?
A: Yes

SC-053

Q: Trailing zeros in 100!?
A: 24

SC-054

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-055

Q: LCM(4,6)?
A: 12

SC-056

Q: Fast power complexity?
A: O(log n)

SC-057

Q: Sieve complexity?
A: O(n log log n)

SC-058

Q: nCr(5,2)?
A: 10

SC-059

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-060

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-061

Q: GCD of 48 and 18?
A: 6

SC-062

Q: Is 29 prime?
A: Yes

SC-063

Q: Trailing zeros in 100!?
A: 24

SC-064

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-065

Q: LCM(4,6)?
A: 12

SC-066

Q: Fast power complexity?
A: O(log n)

SC-067

Q: Sieve complexity?
A: O(n log log n)

SC-068

Q: nCr(5,2)?
A: 10

SC-069

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-070

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-071

Q: GCD of 48 and 18?
A: 6

SC-072

Q: Is 29 prime?
A: Yes

SC-073

Q: Trailing zeros in 100!?
A: 24

SC-074

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-075

Q: LCM(4,6)?
A: 12

SC-076

Q: Fast power complexity?
A: O(log n)

SC-077

Q: Sieve complexity?
A: O(n log log n)

SC-078

Q: nCr(5,2)?
A: 10

SC-079

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-080

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-081

Q: GCD of 48 and 18?
A: 6

SC-082

Q: Is 29 prime?
A: Yes

SC-083

Q: Trailing zeros in 100!?
A: 24

SC-084

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-085

Q: LCM(4,6)?
A: 12

SC-086

Q: Fast power complexity?
A: O(log n)

SC-087

Q: Sieve complexity?
A: O(n log log n)

SC-088

Q: nCr(5,2)?
A: 10

SC-089

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-090

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-091

Q: GCD of 48 and 18?
A: 6

SC-092

Q: Is 29 prime?
A: Yes

SC-093

Q: Trailing zeros in 100!?
A: 24

SC-094

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-095

Q: LCM(4,6)?
A: 12

SC-096

Q: Fast power complexity?
A: O(log n)

SC-097

Q: Sieve complexity?
A: O(n log log n)

SC-098

Q: nCr(5,2)?
A: 10

SC-099

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-100

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-101

Q: GCD of 48 and 18?
A: 6

SC-102

Q: Is 29 prime?
A: Yes

SC-103

Q: Trailing zeros in 100!?
A: 24

SC-104

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-105

Q: LCM(4,6)?
A: 12

SC-106

Q: Fast power complexity?
A: O(log n)

SC-107

Q: Sieve complexity?
A: O(n log log n)

SC-108

Q: nCr(5,2)?
A: 10

SC-109

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-110

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-111

Q: GCD of 48 and 18?
A: 6

SC-112

Q: Is 29 prime?
A: Yes

SC-113

Q: Trailing zeros in 100!?
A: 24

SC-114

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-115

Q: LCM(4,6)?
A: 12

SC-116

Q: Fast power complexity?
A: O(log n)

SC-117

Q: Sieve complexity?
A: O(n log log n)

SC-118

Q: nCr(5,2)?
A: 10

SC-119

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-120

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-121

Q: GCD of 48 and 18?
A: 6

SC-122

Q: Is 29 prime?
A: Yes

SC-123

Q: Trailing zeros in 100!?
A: 24

SC-124

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-125

Q: LCM(4,6)?
A: 12

SC-126

Q: Fast power complexity?
A: O(log n)

SC-127

Q: Sieve complexity?
A: O(n log log n)

SC-128

Q: nCr(5,2)?
A: 10

SC-129

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-130

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-131

Q: GCD of 48 and 18?
A: 6

SC-132

Q: Is 29 prime?
A: Yes

SC-133

Q: Trailing zeros in 100!?
A: 24

SC-134

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-135

Q: LCM(4,6)?
A: 12

SC-136

Q: Fast power complexity?
A: O(log n)

SC-137

Q: Sieve complexity?
A: O(n log log n)

SC-138

Q: nCr(5,2)?
A: 10

SC-139

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-140

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-141

Q: GCD of 48 and 18?
A: 6

SC-142

Q: Is 29 prime?
A: Yes

SC-143

Q: Trailing zeros in 100!?
A: 24

SC-144

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-145

Q: LCM(4,6)?
A: 12

SC-146

Q: Fast power complexity?
A: O(log n)

SC-147

Q: Sieve complexity?
A: O(n log log n)

SC-148

Q: nCr(5,2)?
A: 10

SC-149

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-150

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-151

Q: GCD of 48 and 18?
A: 6

SC-152

Q: Is 29 prime?
A: Yes

SC-153

Q: Trailing zeros in 100!?
A: 24

SC-154

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-155

Q: LCM(4,6)?
A: 12

SC-156

Q: Fast power complexity?
A: O(log n)

SC-157

Q: Sieve complexity?
A: O(n log log n)

SC-158

Q: nCr(5,2)?
A: 10

SC-159

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-160

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-161

Q: GCD of 48 and 18?
A: 6

SC-162

Q: Is 29 prime?
A: Yes

SC-163

Q: Trailing zeros in 100!?
A: 24

SC-164

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-165

Q: LCM(4,6)?
A: 12

SC-166

Q: Fast power complexity?
A: O(log n)

SC-167

Q: Sieve complexity?
A: O(n log log n)

SC-168

Q: nCr(5,2)?
A: 10

SC-169

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-170

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-171

Q: GCD of 48 and 18?
A: 6

SC-172

Q: Is 29 prime?
A: Yes

SC-173

Q: Trailing zeros in 100!?
A: 24

SC-174

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-175

Q: LCM(4,6)?
A: 12

SC-176

Q: Fast power complexity?
A: O(log n)

SC-177

Q: Sieve complexity?
A: O(n log log n)

SC-178

Q: nCr(5,2)?
A: 10

SC-179

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-180

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-181

Q: GCD of 48 and 18?
A: 6

SC-182

Q: Is 29 prime?
A: Yes

SC-183

Q: Trailing zeros in 100!?
A: 24

SC-184

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-185

Q: LCM(4,6)?
A: 12

SC-186

Q: Fast power complexity?
A: O(log n)

SC-187

Q: Sieve complexity?
A: O(n log log n)

SC-188

Q: nCr(5,2)?
A: 10

SC-189

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-190

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)

SC-191

Q: GCD of 48 and 18?
A: 6

SC-192

Q: Is 29 prime?
A: Yes

SC-193

Q: Trailing zeros in 100!?
A: 24

SC-194

Q: 153 Armstrong?
A: Yes: 1+125+27=153

SC-195

Q: LCM(4,6)?
A: 12

SC-196

Q: Fast power complexity?
A: O(log n)

SC-197

Q: Sieve complexity?
A: O(n log log n)

SC-198

Q: nCr(5,2)?
A: 10

SC-199

Q: Digital root of 493?
A: 7 (4+9+3=16, 1+6=7)

SC-200

Q: φ(12)?
A: 4 (1,5,7,11 coprime to 12)