Question

Find the HCF of the following by using Euclid division lemma.
i. 50 and 70
ii. 96 and 72
iii. 300 and 550
iv. 1860 and 2015

Answer 1

1. 50 and 70
70=1x50+20
50=20x2+10
20=10x2+0
HCF=10

2.96 and 72
96=72x1+24
72=24x3+0
HCF=24

3.300 and 550
550=300x1+250
300=250x1+50
250=50x5+0
HCF=50

4.1860 and 2015
2015=1860x1+155
1860=155x12+0
HCF=155

Answer 2

Answer:

(i). HCF = 10

(ii). HCF = 24

(iii). HCF = 50

(iv). HCF = 155

step-by-step explanation:

The largest amount that divides each of the two numbers is known as the HCF, or highest common factor. HCF is also known by the titles The Greatest Common Measure (GCM) and The Greatest Common Divisor (GCD). The least common multiple, or LCM, is used to determine the smallest similar multiple of any two numbers. LCM and HCM are two separate techniques.

Each number should be written as the sum of its prime factors. This approach is known as prime factorization. Name the components thatBoth integers now have something in common. The HCF is the sum of all identical prime factors ( use the lower power of each common factor)

(i). 50 and 70

for given two positive integers a>b;

$70 = 50*1+20\\a = 70, b = 50, q = 1, r = 20$

now consider $50,20$

$50 = 20*2+10\\a = 50, b = 20, q = 2, r = 10$

now taking $20,10$

$20 = 10*2+0$

therefore, the remainder is zero

$10$ is the $HCF$ of $70,50$

(ii). 50 and 70

$96 = 72*1+24\\72 = 24*3+0\\HCF = 24$

(iii). 300 and 550

$550 = 300*1+250\\300 = 250*1+50\\250 = 50*5+0\\HCF = 50$

(iv). 1860 and 2015

$2015 = 1860*1+155\\1860 = 155*12+0\\HCF = 155$

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