Find the largest number which divides 245 and 1029

Asked by admin @ 12/08/2021 in Math viewed by 297 People

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.

Answered by admin @ 12/08/2021

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....

Find the largest number which divides 245 and 1029

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