# Find the odd numbers lying between 1000 and 1500,the H.C.F of which is 157. We are asked to find odd numbers between 1000 and 1500 such that 157 is their greatest common factor. Since 157 is prime, we need only look at multiples of 157:

157x7=1099

157x8=1256

157x9=1413

These are the only multiples of 157 in the required range. The question further stipulates that...

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We are asked to find odd numbers between 1000 and 1500 such that 157 is their greatest common factor. Since 157 is prime, we need only look at multiples of 157:

157x7=1099

157x8=1256

157x9=1413

These are the only multiples of 157 in the required range. The question further stipulates that the numbers be odd, so we discard 1256.

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The numbers we seek are 1099 and 1413

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