Let d be the HCF of 24 and 36 find the two numbers a and b such that d

1.	Let d be the HCF of 24 and 36 find the two numbers a and b such that d = 24a+36b
Answer» Let d be the HCF of 24 and 36.24 = 23{tex}\\times{/tex}336 = 22{tex}\\times{/tex}32HCF = 22{tex}\\times{/tex}3 = 12{tex}\\Rightarrow{/tex}{tex}d = 12{/tex}Now {tex}d = 24a + 36b{/tex}{tex}12 = 24a + 36b{/tex}When\xa0{tex} a = -1{/tex} and {tex}b = 1{/tex}, we get12 = 24{tex}\\times{/tex}(-1) + 36{tex}\\times{/tex}(1)= -24 + 3612 = 12So, a = -1 , b = 1 satisfy the equation d = 24a + 36b{tex}\\therefore{/tex} One possible value of a and b is -1 and 1.

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