PRIME NUMBERS. Every prime number is an odd number and has for its unit figure 1, 3, 7, or 9; any odd number that has 5 for its unit figure is divisible by 5, and is not a prime number. The prime factors of any number less than 1,000 may be found from the following table. If the number is odd and does not end with 5, the factors are given directly; thus, the prime factors of 357 are 3, 7, and 17; those of 931 are 7, 7, and 19, the exponent 2 of the 7 indicating that 7 is used twice as a factor. If a number is a prime number, the space beside it is blank; thus, 317 and 859 are prime numbers. To find the prime factors of an odd number that has 5 for the unit figure, divide by 5 until a quotient is obtained which does not have 5 for a unit figure; the factors of this quotient are then found from the table, and with the 5's already used as divisors constitute the prime factors. For example, to find the prime factors of 5,775 proceed as follows: 5,775 ÷ 5 1,155; 1,155÷5 from the table, 231 3X7X 11; hence, 5,775 7 X 11. If the number is even, divide it by 2, the quotient by 2, and so on until an odd quotient is reached; then find the prime factors of the quotient from the table. The process of finding the prime factors of 936 is as follows: 9362 from table. == = 231; 3X5X5X 468; 468 ÷ 2 = 234; 234 -2 = 117; 117 = 32 X 13, Hence, 936 = = 23 × 32 × 13 = 2×2×2×3× 3 × 13. |