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We also have the rule that 10 x + y is divisible iff x + 4 y is divisible by 13. For example, to test the divisibility of 1761 by 13 we can reduce this to the divisibility of 461 by the first rule. Using the second rule, this reduces to the divisibility of 50, and doing that again yields 5. So, 1761 is not divisible by 13.
Dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions. A person who has calculated the power output of a car to be 700 kJ may have omitted a factor, since the unit joules is a measure of energy, not power (energy per unit time).
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The following laws can be verified using the properties of divisibility. They are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic ...
In base 10, this is simplest for =,,, where higher digits except for the unit digit vanish (since 2 and 5 divide powers of 10), which corresponds to the familiar fact that the divisibility of a decimal number with respect to 2, 5, and 10 can be checked by the last digit.
The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10. In mathematics, a divisor of an integer , also called a factor of , is an integer that may be multiplied by some integer to produce . [1] In this case, one also says that is a multiple of .