Comprehensive Study Guide on Divisibility Tests: 3, 4, 6, 8, and 9

Vocabulary flashcards covering divisibility rules and tests for 3, 4, 6, 8, 9, and 10 from Chapter 1: Basic Computation.

Divisibility Test of 4

A test stating that an integer is divisible by $4$ if its last two digits are $00$ or a multiple of $4$.

Condition for Non-Divisibility by 4

The condition where an integer is not divisible by $4$ if its last two digits are neither $00$ nor a multiple of $4$.

Divisibility Test of 8

A test stating that an integer is divisible by $8$ if its last three digits are $000$ or a multiple of $8$.

Condition for Non-Divisibility by 8

The condition where an integer is not divisible by $8$ if its last three digits are neither $000$ nor a multiple of $8$.

Divisibility Test of 10

A test establishing that an integer is divisible by $10$ if its last digit is $0$.

Divisibility Test of 3

A rule stating that an integer is divisible by $3$ if the sum of all its digits is a multiple of $3$.

Divisibility Test of 6

A test stating that an integer is divisible by $6$ if it is an even number and is divisible by $3$.

Condition for Non-Divisibility by 6

The condition where an integer is not divisible by $6$ if it is not an even number or is not divisible by $3$.

Characteristics of Multiples of 6

Integers that are both even numbers and divisible by $3$.

Units Place Requirement for Divisibility by 6

The condition requiring an even digit to be placed at the units place of a number whose digits sum to a multiple of $3$, ensuring that the number is an even number and therefore divisible by $6$.

Divisibility Test of 9

A test stating that an integer is a multiple of $9$ (divisible by $9$) if the sum of all its digits is a multiple of $9$.

Hugo's Claim

The assertion that if a number is divisible by both $2$ and $4$, then it must be divisible by $8$, which can be disproven with a counterexample (such as $12$ or $20$).