Name: Properties of Division of Integers
Uploaded: 2019-07-19
Duration: 8 min 15 s
Description: Learn everything you'll need to know about the properties of the division of integers in a quick and short lesson that'll help you master the concept.

Question

What numbers between

1 and 10

are factors of

123456

.

Accepted Answer

Given number: $123456$ ,

Divisibility rules:

If a number is even or a number whose last digit is an even number i.e. $2, 4, 6, 8$ including $0$ , it is always completely divisible by $2$ .

Divisibility rule for $3$ states that a number is completely divisible by $3$ if the sum of its digits is divisible by $3$ .

If the last two digits of a number are divisible by $4$ , then that number is a multiple of $4$ and is divisible by $4$ completely.

Numbers, which last with digits, $0$ or $5$ are always divisible by $5$ .

Numbers which are divisible by both $2$ and $3$ are divisible by $6$ . That is, if the last digit of the given number is even and the sum of its digits is a multiple of $3$ , then the given number is also a multiple of $6$ .

If the last three digits of a number are divisible by $8$ , then the number is completely divisible by $8$ .

The rule for divisibility by $9$ is similar to divisibility rule for $3$ . That is, if the sum of digits of the number is divisible by $9$ , then the number itself is divisible by $9$ .

Divisibility rule for $10$ 10 states that any number whose last digit is $0$ , is divisible by $10$ .

$1$ is a factor of every number.

From above rules we can observe that,

The given number is divisible by $2$ because last digit of it is even.

The given number is divisible by $3 and 9$ because the sum of digits of given number is divisible by $3 and 9$ .

The given number is divisible by $6$ because it is divisible by both $2 and 3$ .

The given number is divisible by $8$ because number formed by last three digits of it is divisible by $8$ .

The given number is divisible by $4$ because number formed by last two digits of it is divisible by $4$ .

Hence, there are seven factors of given number between $1 and 10$ , i.e., $1, 2, 3, 4, 6, 8, 9$ .

What numbers between $1 and 10$ are factors of $123456$ .

Important Questions on Integers

Learn and Prepare for any exam you want !

What numbers between 1 and 10 are factors of 123456.

Important Questions on Integers

Learn and Prepare for any exam you want !

What numbers between $1 and 10$ are factors of $123456$ .