Module 3 · Number System
Chapter 32: HCF
Number System
2 topics
What this chapter covers
The 2 topics below make up HCF on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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🎯 Topic tests
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📝 Chapter test
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Formula Reference Sheet
This chapter
Core HCF rules
| Prime factorization HCF | product of each common prime raised to its LOWEST power |
|---|---|
| Euclidean algorithm | HCF(a, b) = HCF(b, a mod b), until remainder = 0 |
| HCF × LCM (two numbers) | HCF(a, b) × LCM(a, b) = a × b |
| HCF of fractions | HCF(numerators) / LCM(denominators) |
| Co-prime check | a, b are co-prime ⇔ HCF(a, b) = 1 |
CAT application formulas
| Largest tile / container | side or capacity = HCF of the given dimensions |
|---|---|
| Greatest number dividing a, b, c exactly | HCF(a, b, c) |
| Greatest number leaving same remainder r | HCF(a − r, b − r, c − r) |
| Greatest number leaving remainders r1, r2, r3 | HCF(a − r1, b − r2, c − r3) |
| HCF scales with a common factor | HCF(ka, kb) = k × HCF(a, b) |
CAT reference
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