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No they do not, take a big Prime number and compare it to a smaller composite number. The number 6833 as only two factors (divisors), namely 1 and itself. But the number 68 which is much smaller has more factors or divisors. 68 has 2 and 4 and 17 and 1 and itself which is already more divisors than 6833.

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Q: Do bigger numbers necessarily have more divisors?
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