Prime Numbers

There are quite a few.

101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997

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36 = 729

35656666666.654

64

None no prime number can be even because it could be divided by 2

233,357 is a prime number. Its only factors are one and itself. Draw it any way you like, unless you mean 2 x 3 x 3 x 3 x 5 x 7. That's the prime factorization of 1890.

There are infinitely many pairs.

Lets us start with addition/subtraction:

183+183, 184+182, 185+181, ... , 365+1, 366+0, 367-1, 368-2, ... and on and on.

Then introduce numbers to 1 decimal place:

183.1+182.9, 183.2+182.8, 183.3+182.7, and so on - forever.

And then two decimal places:

183.01+182.99, 183.02+182.98 and so on.

And then 3 decimal places, 4, and so on to infinitely many decimal places.

Next, look at multiplication/division

1*366, 2*183, 3*122, 4*91.5, and so on

and then start introducing fractions.

To find a prime factorization, divide a composite number and its factors by prime numbers until all the factors are prime. Many people find factor trees helpful in visualizing this process. Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 is the prime factorization of 210.

No.

The prime factors of 1,105 are: 5, 3, 17

63 = 9 x 7 which would be 32 x 71

All numbers that only have one and itself as factors are prime. So to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number.

70

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

That's an infinite list.

The prime factors of 40 are: 2 and 5.

7546 = 2 * 7 * 7 * 7 * 11 = 2 * 73 * 11

2 x 32 = 18

1323 is not prime. 1323 = 3 * 3 * 3 * 7 * 7

45 = 3 * 3 * 5

3100000

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

6 and -5

369 is composite.

Because its the closest prime number to 69 without going over.