It is often useful to know whether a number divides another number. To check divisibility, one can always do the division out by hand and see if the result is a whole number. However, if the number we are dividing is large, this becomes very difficult. There are some divisibility rules which make this task much easier--these rules allow us to determine whether a number is divisible by another number without having to carry out the division.
Divisibility by 1A number does not change when it is divided by 1. Therefore, every whole number is divisible by 1.
Divisibility by 2, 4, and 8All even numbers are divisible by 2. Therefore, a number is divisible by 2 if it has a 0, 2, 4, 6, or 8 in the ones place. For example, 54 and 2,870 are divisible by 2, but 2,221 is not divisible by 2.
A number is divisible by 4 if its last two digits are divisible by 4. For example, 780, 52, and 80,744 are divisible by 4, but 7,850 is not divisible by 4. To check whether a number is divisible by 4, just divide the last two digits of the number by 4. If the result is a whole number, then the original number is divisible by 4.
A number is divisible by 8 if its last three digits are divisible by 8. For example, 880 and 905,256 are divisible by 8 but 74,513 is not divisible by 8. To check divisibility by 8, divide the last three digits of the number by 8. If the result is a whole number, then the original number is divisible by 8.
Divisibility by 3, 6, and 9A number is divisible by 3 if its digits add up to a number divisible by 3. For example, 671,451 is divisible by 3 because 6 + 7 + 1 + 4 + 5 + 1 = 24 , and 24 is divisible by 3. 84,950 is not divisible by 3, because 8 + 4 + 9 + 5 + 0 = 26 , and 26 is not divisible by 3.
A number is divisible by 6 if it is divisible by 2 and 3. In other words, a number is divisible by 6 if its digits add up to a number divisible by 3 and it ends with an even number. 671,451 (our previous example) is divisible by 3, but not by 2, because 1 is not an even number. Therefore, 671,451 is not divisible by 6. On the other hand, 789,312 is divisible by 6, because 7 + 8 + 9 + 3 + 1 + 2 = 30 , which is divisible by 3, and its last digit is 2, which is even.
A number is divisible by 9 if its digits add up to a number divisible by 9. For example, 91,458 is divisible by 9 because 9 + 1 + 4 + 5 + 8 = 27 and 27 is divisible by 9. 18,453 is not divisible by 9 because 1 + 8 + 4 + 5 + 3 = 21 and 21 is not divisible by 9.
Divisibility by 5A number is divisible by 5 if it ends in 0 or 5. For example, 875 and 600 are divisible by 5, but 76,508 is not divisible by 5.
Divisibility by 10A number is divisible by 10 if it ends in 0. For example, 65,110 and 90 are divisible by 10, but 6,007 is not divisible by 10.
Note: Because a number divided by itself always yields 1, a number is always divisible by itself. For example, 7 is divisible by 7 and 8,374 is divisible by 8,374.
Note: No number is divisible by a number greater than itself.
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When one number is divisible by another number, it means that the first number can be divided by the second number without leaving a remainder. In other words, the division operation results in a whole number without any fraction.
No.
The number of neutrons is different.
Neutrons.
one thickness that lies on top of or under another one.
The atomic number is equal to the number of protons in the atomic nucleus. It is an individual characteristic.