What are divisible criteria?

First of all, it is important to say that these criteria can only be applied to natural numbers (whole positive numbers).

These criteria are used to know if a certain number can be divided by another one without being necessary to make a calculation. For instance, it is possible to see if 5492 can be divided by 3 without making an operation.

What does it mean when we say that a number can be divided by another one?

It happens when the division is made and its result is a whole number and the remainder is zero. For instance, number 12 can be divided by 3 because the result is 4 and the remainder is zero. However, 12 cannot be divided by 5, since the reminder is not 0. According to the mathematical language: “If D and d are whole numbers, it is said that D (dividend) can be divided by d (divisor) if there is a natural number q (quotient) so that d x q = D.”

What are the divisible criteria of a certain number by 1?

What a silly question!!! Everybody knows that every number can be divided by 1.

What are the divisible criteria of a certain number by 2?

Every number whose unit digit is 0,2,4,6 or 8 can be divided by 2 (it means the number is an even one). For instance:

• 456 (it ends in 6) can be divided by 2;
• 357 (it ends in 7) cannot be divided by 2;
• 280 (it ends in 0) can be divided by 2;
• 91 (it ends in 1) cannot be divided by 2.

What are the divisible criteria of a certain number by 3?

If the sum of the digits can be divided by 3, the number can also be divided by 3. For instance:

• 624 (6+2+4=12) (12 can be divided by 3) can be divided by 3;
• 431 (4+3+1=8) (8 cannot be divided by 3) cannot be divided by 3;
• 91 (9+1=10) (10 cannot be divided by 3) cannot be divided by 3;
• 4671 (4+6+7+1=18) (18 can be divided by 3) can be divided by 3.

What are the divisible criteria of a certain number by 4?

If both last digits can be divided by 4, the number can also be divided by 4. For instance:

• 1020 (20 can be divided by 4) can be divided by 4;
• 721 (21 cannot be divided by 4) cannot be divided by 4;
• 639 (39 cannot be divided by 4) cannot be divided by 4;
• 836 (36 can be divided by 4) can be divided by 4.

What are the divisible criteria of a certain number by 5?

This is one of the easiest situations. If the unit digit of a certain number is 0 or 5, the number can be divided by 5. For instance:

• 380 (it ends in 0) can be divided by 5;
• 264 (it ends in 4) cannot be divided by 5;
• 2175 (it ends in 5) can be divided by 5;
• 403 (it ends in 3) cannot be divided by 5.

What are the divisible criteria of a certain number by 6?

If a number can be divided by 2 and 3, it can also be divided by 6. For instance:

• 620 (it ends in 0 and it can be divided by 2) (6+2+0=8 cannot be divided by 3) cannot be divided by 6;
• 1224 (it ends in 4 and it can be divided by 2) (1+2+2+4=9 and it can be divided by 3) can be divided by 6;
• 295 (it ends in 5 and it cannot be divided by 2) cannot be divided by 6;
• 78 (it ends in 8 and it can be divided by 2) (7+8=15 and it can be divided by 3) can be divided by 6.

What are the divisible criteria of a number by 7?

This is one of the most difficult situations. We have to separate the number from its last digit. If the first set of the separated digits minus the double of the last digit is a multiple of seven, the original number can be divided by 7. For instance:

• 624 (62-4x2=54) (54 cannot be divided by 7) cannot be divided by 7;
• 525 (52-5x2=42) (42 can be divided by 7) can be divided by 7;
• 429 (42-9x2=24) (24 cannot be divided by 7) cannot be divided by 7;
• 707 (70-7x2=56) (56 can be divided by 7) can be divided by 7.

What are the divisible criteria of a certain number by 8?

The only criteria a know is very difficult to apply and so it is not worth explaining it.

What are the divisible criteria of a certain number by 9?

If the sum of the number digits can be divided by 9, the number can also be divided by 9. For instance:

• 2079 (2+0+7+9=18) (18 can be divided by 9) can be divided by 9;
• 275 (2+7+5=14) (14 cannot be divided by 9) cannot be divide by 9;
• 9945 (9+9+4+5=27) (27 can be divided by 9) can be divided by 9;
• 7824 (7+8+2+4=21) (21 cannot be divided by 9) cannot be divided by 9.

What are the divisible criteria of a number by 10?

This is another very easy situation. If a unit digit of a number is 0, the number can be divided by 10. For instance:

• 350 (it ends in 0) can be divided by 10;
• 724 (it ends in 4) cannot be divided by 10;
• 900 (it ends in 0) can be divided by 10;
• 43 (it ends in 3) cannot be divided by 10.

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