formula_165. Multiplying an integer by its formula_20-adic absolute value cancels out the factors of formula_20 in its factorization, leaving only the other primes. Just as the distance between two real numbers can be measured by the absolute value of their distance, the distance between two rational numbers can be measured by their formula_20-adic distance, the formula_20-adic absolute value of their difference. For this definition of distance, two numbers are close together (they have a small distance) when their difference is divisible by a high power of formula_20. In the same way that the real numbers can be formed from the rational numbers and their distances, by adding extra limiting values to form a complete field, the rational numbers with the formula_20-adic distance can be extended to a different complete field, the formula_20-adic numbers.