Question

1 fill in the blank 1 point
a method for checking or testing to see if a counting number is divisible by another counting number, without actually carrying out the division, is called a
2 multiple answer 1 point
determine which of the following numbers are divisible by 3. use the divisibility test for 3 to check each. choose every number that is divisible by 3.
987654320
123123
906028
906030
123456789
110101
123124
1101

Explanation:

Step1: Define the divisibility rule

A method to test divisibility without division is a divisibility rule.

Step2: Test 987654320 for divisibility by 3

Sum digits: $9+8+7+6+5+4+3+2+0=44$. $44\div3=14$ remainder $2$, not divisible.

Step3: Test 123123 for divisibility by 3

Sum digits: $1+2+3+1+2+3=12$. $12\div3=4$, divisible.

Step4: Test 906028 for divisibility by 3

Sum digits: $9+0+6+0+2+8=25$. $25\div3=8$ remainder $1$, not divisible.

Step5: Test 906030 for divisibility by 3

Sum digits: $9+0+6+0+3+0=18$. $18\div3=6$, divisible.

Step6: Test 123456789 for divisibility by 3

Sum digits: $1+2+3+4+5+6+7+8+9=45$. $45\div3=15$, divisible.

Step7: Test 110101 for divisibility by 3

Sum digits: $1+1+0+1+0+1=4$. $4\div3=1$ remainder $1$, not divisible.

Step8: Test 123124 for divisibility by 3

Sum digits: $1+2+3+1+2+4=13$. $13\div3=4$ remainder $1$, not divisible.

Step9: Test 1101 for divisibility by 3

Sum digits: $1+1+0+1=3$. $3\div3=1$, divisible.

Answer:

1. divisibility rule

2.

• 123123
• 906030
• 123456789
• 1101