Math, asked by ustachi1nturitu, 1 year ago

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 nikitasingh79
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....
Attachments:
Answered by vanshd994
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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