Find the h.c.f of 176 and …

Given numbers are 176 and 38220.
Here, 38220 > 17
By using Euclid's division lemma, we get 
a = bq + r, where 0<_r < b. Here a as dividend, b as divisor, q as quotient and r as remainder
Dividend = divisor {tex}\times{/tex} quotient + remainder


dividend = divisor {tex}\times{/tex} quotient + remainder
38220 = (176 {tex}\times{/tex} 217) + 28   
Here r = 28 {tex}\ne{/tex} 0  and b = 176
On taking 176 as the new dividend and 28 as the new divisor and then apply Euclid's division lemma, we get
176 = (28 {tex}\times{/tex} 6) + 8
Here remainder = 8 {tex}\ne{/tex} 0
So, on taking 28 as dividend and 8 as the divisor and then apply Euclid's division lemma, we get
28 = (8 {tex}\times{/tex} 3) + 4
Again, remainder = 4 {tex}\ne{/tex} 0
On taking 8 as the dividend and 4 as the divisor and then apply Euclid's division lemma, we get 8 = ( 4 {tex}\times{/tex} 2) + 0 
Here, remainder = 0 and last divisor is 4.
Hence, HCF of 176 and 38220 is 4.