# 4th Class Mathematics Factors and Multiples Factor and Multiples

Factor and Multiples

Category : 4th Class

Factor and Multiples

Synopsis

• When two or more numbers are multiplied, a product is obtained. Each number is called a factor of the product. The product is called

• Multiples of a multiple of each of the numbers.

e.g., $\text{5 }\times \text{ 7 }\times \text{ 9}=\text{315}$

5, 7 and 9 are factors of 315 and 315 is a multiple of each of 5, 7 and 9.

• The multiples which appear in both the lists of multiples of the given numbers are called their common multiples.

e.g.., Multiples of

$\therefore$ Common multiples of 2 and 4 are 4, 8, 12, ......

• A number is said to be the factor of another if it can divide the other completely. So, a factor is also called the divisor. The factors of a number are less than or equal to the number.
• 1 is a factor of every number. Every number is a factor of itself.
• A number is the greatest factor of itself and 1 is the least factor of a number.
• Every multiple of a number is greater than or equal to the number itself.
• Every number is a multiple of 1.
• Every number is a multiple of itself.
• There is no greatest multiple of a number.

Even Number:

A number which when divided by 2, leaves zero as remainder, is an even number.

e.g., 2, 4, 6, 8, 10,...

Odd Number:

A number which when divided by 2, leaves one as remainder, is an odd number.

e.g., 1, 3, 5, 7, 9,...

Prime Number:

• A number that has only 2 factors, that is, 1 and the number itself is known as a prime number, g., 2, 3, 5, 7, 11, ...

Composite Number:

• A number which has more than two factors is called a composite number.
• g., 4, 6, 8, 9, . ..
• Number 1 has only one factor. It is neither prime nor composite. It is called a unique number.
• 2 is the only even prime number and also the smallest prime number.
• All prime numbers except 2 are odd numbers.
• All even numbers except 2 are composite numbers.

Co-prime Numbers:

• 4 Two numbers which have no other common factor except 1 are called co-prime numbers. g., 3, 4; 4,7; etc.,

Twin-prime Numbers:

• Consecutive prime numbers with a difference of 2 between them are called twin primes.

e.g.,   3, 5; 5, 7; 11, 13; etc.,

The factors which divide both the given numbers are called their common factors.

e.g.,   Factors of 27 are and 27.

Factors of 18 are and 18.

$\therefore$  Common factors of 27 and 18 are 1, 3 and 9.

Rules of divisibility:

• A number is divisible by 2 if the digit in its ones place is any of 0,2,4,6 or 8.
• A number is divisible by 3, if the sum of its digits is divisible by 3.
• A number is divisible by 4, if the number formed by the digits in its tens and units place i.e., last 2 digits is divisible by 4.
• A number is divisible by 5, if the digit in its ones place is either 0 or 5.
• A number is divisible by 9, if the sum of its digits is divisible by 9.
• A number is divisible by 10, if the digit in its ones place is 0.

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