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The HCF is 24, so both numbers will have 24 as a factor. This means both will be multiples of 24 so we can simply divide 144 by 24 to find which multiple. Do this and you get:
144/24 = 6
So the number multiple of 24 each number is needs to add up to 6. However, it cannot be 3 and 3 or 2 and 4 as then the numbers would have a greater HCF. Thus it must be 5x24 and 1x24, or 24 and 120.
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