Question

7. Two ropes are of length 64 cm and 80 cm. Both are to be cut into pieces
equal length. What should be the maximum length of the pieces?
The Fundamental Theorem of Arithmetic
our earlier classes, you have seen that any natural number can be written
duct of its prime factors. For instance, 2 = 2.4 = 2 * 2,253 = 11 * 23, and so
v, let us try and look at natural numbers from the other direction. That is, can
aral number be obtained by multiplying prime numbers? Let us see.
Take any collection of prime numbers, say 2, 3, 7, 11 and 23. If we mult
ne or all of these numbers, allowing them to repeat as many times as we
can produce a large collection of positive integers (In fact, infinitely ma
us list a few :
7 * 11 * 23 = 1771
3 x 7 x 11 x 23 = 5313
2 * 3 * 7 * 11 * 23 = 10626 23 * 3 * 7 = 8232
22 * 3 * 7 * 11 x 23 = 21252
so on.
Now, let us suppose your collection of primes includes all the possible pr
is your guess about the size of this collection? Does it contain only a
er of integers, or infinitely many? Infact, there are infinitely many primes.​

Answer 1

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