Question

Find the HFC of the following by using euclid division lemma 50 and 70, 196 and 72, 300 and 550, 1860 and 2015

Answer 1

According to the Euclid Division Lemma,
a=bq+r  (0<_r<q)
Let,
a=70 and b=50
substitute in a=bq+r
70=50*1+20
50=20*2+10
20=10*2+0
Hence the GCF of 50 and 70 is 10


According to the Euclid Division Lemma,
a=bq+r  (0<_r<q)
Let,
a=196 and b=72
substitute in a=bq+r

196=70*2+56
70=56*1+14
56=14*4+0
Hence the GCF of the 196 and 72 is 14.



According to the Euclid Division Lemma,
a=bq+r  (0<_r<q)
Let,
a=550 and b=300
substitute in a=bq+r
550=300*1+250
300=250*1+50
250=50*5+0
Hence,the GCF of 550 and 300 is 50





According to the Euclid Division Lemma,
a=bq+r  (0<_r<q)
Let,
a=2015 and b=1860
substitute in a=bq+r
2015=1860*1+55
1860=55*33+45
55=45*1+10
45=10*4+5
10=5*2+0
Hence,the GCF is 5.