Last Digit in a Product of Primes

Number Theory Level 1

If you multiply all primes less than 100, what would the last digit be?

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Andrew Ellinor by Andrew Ellinor , 33, USA

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3 solutions

Andrew Ellinor
Oct 12, 2015

The first 100 primes contain both 2 and 5, so their product will product a factor of ten, meaning the last digit will be 0.

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Same solution. But more, can you find the last two digits?

Kenneth Gravamen - 5 years, 8 months ago

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The last two digits are 10 for 2.3.5.7.11.13.17.19.23.29.31.37.41.43.47.53.59..61.67.71.73.79.83.89.97 (mod 100) becomes 690 (mod 100)= 90 (mod 100) after a little calculation

Devendra Kumar Singh - 5 years, 8 months ago

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You forgot 89 in your list. So, actually, the last two digits are 90

Mateo Matijasevick - 5 years, 7 months ago

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@Mateo Matijasevick – Thanks for pointing out the missing prime.

Devendra Kumar Singh - 5 years, 7 months ago

What exactly did you mean? I took all possible last digits and multiplied them to get 9 5 7 3 2=1890.

Zyberg NEE - 5 years, 8 months ago

Thought the same thing.

Sam Maltia - 5 years, 8 months ago
Sudip Dey
Oct 14, 2015

If we consider only the prime numbers within 1 to 10....those are 1, 2, 3, 5, 7........and multiplication of 1 x 2 x 3 x 5 x 7 =210.....whose last digit (of 210) is 0.....hence last digit of by multiplying all the primes less than 100 will also be 0.

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I solved it similarly, just instead of taking first prime numbers, I took the last possible digits of them all (looking at that image) which are 9,5,7,3,2, multiplying them results in 1890, so the answer will be 0.

Zyberg NEE - 5 years, 8 months ago

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9 is not a prime number......can you please explain and elaborate why are you multiplying 9,5,7,3,2?

Sudip Dey - 5 years, 8 months ago

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Because 19, 29, 59, 79, 89 are all prime numbers that end with 9. I multiplied all of the possible last digits. It might be not right (although I got the right answer), but I have no understanding of original solution.

Zyberg NEE - 5 years, 8 months ago
Sirajudheen Mp
Oct 19, 2015

2 and 5 are prime 2x5=10 this give last diigit as zoro

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