# Four digit numbers divisible by 3 and 9 in a relationship

### Multiples, Factors and Powers

/9 = 30 /5 = 54 /3 = 90 /2 = So is indeed divisible by all four numbers. However, you wanted a four digit number. Any multiple of Here are the only possible rectangular arrays for the first four prime numbers: . Yet when their sum 63 is divided by 6, the remainder is 3, and is not 4 + 5 = 9. . The two relationships below between the HCF and the LCM are again best . When a number, and the sum of its digits, are both divided 3, the remainders are the. Divisibility by 3 and 9. All numbers that contain only the digit 9 are divisible by 9. If the sum in the second brackets (3 + 2 + 4) is also divisible by 9, then the.

What is the same about the results of the division in each row? Common multiples and the LCM An important way to compare two numbers is to compare their lists of multiples. Let us write out the first few multiples of 4, and the first few multiples of 6, and compare the two lists. The numbers that occur on both lists have been circled, and are called common multiples. The common multiples of 6 and 8 are 0, 12, 24, 36, 48,… Apart from zero, which is a common multiple of any two numbers, the lowest common multiple of 4 and 6 is These same procedures can be done with any set of two or more non-zero whole numbers.

### Divisibility Rules for 3 and 9

A common multiple of two or more nonzero whole numbers is a whole number that a multiple of all of them. The lowest common multiple or LCM of two or more whole numbers is the smallest of their common multiples, apart from zero. Hence write out the first few common multiples of 12 and 16, and state their lowest common multiple.

Hence write down the LCM of 12, 16 and 24? To determine if a number is prime or composite, follow these steps: Find all factors of the number. If the number has only two factors, 1 and itself, then it is prime. If the number has more than two factors, then it is composite.

The above procedure works very well for small numbers.

Thus we need a better method for determining if a large number is prime or composite. Every number has one and itself as a factor. Thus, if we could find one factor ofother than 1 and itself, we could prove that is composite. One way to find factors of large numbers quickly is to use tests for divisibility.

If one whole number is divisible by another number, then the second number is a factor of the first number. Since 18 is divisible by 9, 9 is a factor of A divisibility test is a rule for determining whether one whole number is divisible by another. Determine if the number is even. It ends in 8, so this number is even. Therefore it is divisible by 2. Add the digits together.

So this number is not divisible by 3. Because this number is only divisible by 2, and not by 3, it is NOT divisible by 6. This number is even and is therefore divisible by 2. Because the number is divisible by 2 and 3, it is also divisible by 6. The Rule for 9: The prime factors of 9 are 3 and 3.

## Divisibility Rules for 3 and 9

So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9. If it is, then the actual number is also divisible by 9. This is done the same way we checked the rule for 3.