Q1.Find the largest number which divides 245 and 1029 leaving remainder 5 in each case. Q2. Prove that if x and y are odd positive integer, x>y then x 2 - y 2 is divisible by 4. Q3. Prove that exactly one out of every three consecutive integers is divisible by 3.
Answers
Answered by
336
Answers of Q.2 & Q.3 are in the attachment...
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1) we have to subtract 5 from each number & then find the H.C.F
245-5=240 & 1029-5=1024
HC.F of 240 & 1024 by Euclid division lemma (a=bq+r)
a=1024 & b=240
a=bq+r
1024= 240*4 +64
240= 64*3 +48
64= 48*1 +16
48 = 16*3 +0
H.C.F is 16
Hence the required number is 16
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Hope this will help you....
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1) we have to subtract 5 from each number & then find the H.C.F
245-5=240 & 1029-5=1024
HC.F of 240 & 1024 by Euclid division lemma (a=bq+r)
a=1024 & b=240
a=bq+r
1024= 240*4 +64
240= 64*3 +48
64= 48*1 +16
48 = 16*3 +0
H.C.F is 16
Hence the required number is 16
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Hope this will help you....
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Answered by
17
Answer:
Answer is 16
Step-by-step explanation:
we have to subtract 5 from each number and then find the H. C. F 245-5=240 and 1029-5=1024
HCF of 240 and 1024 by Euclid division lemman (a = bq+r)
a = 1024 and b = 240
a = bq + r
1024 = 240*4+64
240 = 64*3+48
64 = 48*1+16
48 = 16*3+0
HCF is 16
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