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172,144,102,109
my answer
is this the correct way to find the least number ?
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1$172$ does not leave a remainder of $4$ when divided by $5$? $67$ also doesn't leave a remainder of $4$ when divided by $5$. Have I misunderstood the question? – Henrik supports the community Feb 08 '23 at 12:23
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$172-67 = 105 = 753$. – Henrik supports the community Feb 08 '23 at 13:10
1 Answers
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No. You need
$$ 7(5(3+1)+4)+4=172$$
Work backwards. The smallest number that is $1\pmod3$ is $4$. $4$ is therefore the result of dividing by $5$, and therefore was $24$ before the 'divide by $5$ to leave remainder $4$' operation.
As the next operation is 'divide by $7$ to leave remainder $4$', then $24\times7=168$, and add $4$ to give $172$.
JMP
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Why, please offer some kind of explanation to why that number should staisfy the given criteria. – Henrik supports the community Feb 08 '23 at 12:25
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But the remainder when dividing $172$ by $5$ is $2$, not $4$. – Henrik supports the community Feb 08 '23 at 12:40
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1@Henriksupportsthecommunity; the question in the title says 'successively'. – JMP Feb 08 '23 at 12:42
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Okay, if you perform the subsequent divisions on the integer part of the result of the previous division, I see why this is a solution. I understood the successive divisions to all happen on the original number. – Henrik supports the community Feb 08 '23 at 12:49
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