Find the largest number that divides 455 and 42 with the help of division algorithm.

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Introduction to Euclids Geometry

Question

Find the largest number that divides

455

and

42

with the help of division algorithm.

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i) Start with the larger integer

, 455

42) 455 (10 \to

quotient
420

35 \to

remainder

∴ 455 = (42 \times 10) + 35

(By Euclid's lemma)

ii) Consider

42 \div 35

iii) Consider

35 \div 7

35) 42 (1

7) 35 (5

35 35
7 00

∴ 42 = (35 \times 1) + 7

∴ 35 = (7 \times 5) + 0

\Rightarrow H C F (455, 42) = H C F (42, 35) = H C F (35, 7) = 7

∴ 7

is the largest number that divides

455

and

42