582. A number that has no factors is a prime number. 1, 2, 3, 5, 7, etc., are prime numbers.

583. 1. Name the prime numbers between 10 and 20.

2. Between 20 and 30.

3. Between 30 and 50.

584. Sight Exercises.

4. Between 50 and 70.

5. Between 70 and 100.

Give the prime factors, commencing with the smallest.

GREATEST COMMON DIVISOR.

586. A common factor of two or more numbers is a number that will divide each of them without remainder.

The largest number that is a factor of two or more numbers is called the greatest common divisor.

589. How can you tell that a number is divisible by 2? By 5? A number is divisible by 3 when the sum of its digits (figures) is divisible by 3; it is divisible by 9, when the sum of its digits is divisible by 9.

A number is divisible by 4, when the number expressed by its last two figures is divisible by 4.

When is a number divisible by 25?

590. A fraction is reduced to lowest terms by dividing the numerator and the denominator by their greatest common divisor.

591. Reduce to its lowest terms.

In this example, it is not easy to ascertain by inspection any number that will divide both terms. In such cases, the greatest common divisor is found by dividing the denominator by the numerator. The remainder is divided into the numerator, and each subsequent remainder is divided into the corresponding divisor until there is no longer a remainder. This last divisor is the greatest common divisor of the two numbers.

592. In reducing fractions to lowest terms, the above method of finding the greatest common divisor should not be resorted to if it is possible to get along without it.

593. Reduce to lowest terms:

1. 188

A look at both terms shows that 3 is a common factor. This reduces the fraction to. 41 is a prime number, and is not a factor of 100, so that cannot be reduced to lower terms.

2. 111

4+3+2=9; 6+2+1=9

Since the sum of the digits of each term is divisible by 9, this number is a common factor, and reduces the fraction to §, etc.

Add 141, 73%, 64, 4, 23, 101, 58, 97.

Here we have to find the least common multiple of 3, 9, 7, 14, 6, 14, 2, 12. Rejecting 3, 6, 2 because they are factors of 12; 7, a factor of 14; and one 14, we have to find the least common multiple of

9 14 12

Divide these numbers by a prime number that is exactly contained in any two of them, bringing down the numbers that are not multiples of the divisor.

Taking 2 as a divisor, bring down 9, and write quotients 7 and 6.

3 being a factor of two of the three numbers, 9, 7, 6, is taken as the next divisor. 3 is written as a quotient, 7 is brought down, 2 is a quotient.

As there is no factor common to any two of the numbers, 3, 7, 2, we find the least common multiple by multiplying together the two divisors and these three numbers.