Identifying Multiples of Numbers
Learning Outcomes
- Determine whether a given number is divisible by 2,3,5, or 10
Counting Number | [latex]1[/latex] | [latex]2[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] |
---|---|---|---|---|---|---|---|---|---|---|---|---|
[latex]\text{Multiples of }2[/latex] | [latex]2[/latex] | [latex]4[/latex] | [latex]6[/latex] | [latex]8[/latex] | [latex]10[/latex] | [latex]12[/latex] | [latex]14[/latex] | [latex]16[/latex] | [latex]18[/latex] | [latex]20[/latex] | [latex]22[/latex] | [latex]24[/latex] |
[latex]\text{Multiples of }3[/latex] | [latex]3[/latex] | [latex]6[/latex] | [latex]9[/latex] | [latex]12[/latex] | [latex]15[/latex] | [latex]18[/latex] | [latex]21[/latex] | [latex]24[/latex] | [latex]27[/latex] | [latex]30[/latex] | [latex]33[/latex] | [latex]36[/latex] |
[latex]\text{Multiples of }4[/latex] | [latex]4[/latex] | [latex]8[/latex] | [latex]12[/latex] | [latex]16[/latex] | [latex]20[/latex] | [latex]24[/latex] | [latex]28[/latex] | [latex]32[/latex] | [latex]36[/latex] | [latex]40[/latex] | [latex]44[/latex] | [latex]48[/latex] |
[latex]\text{Multiples of }5[/latex] | [latex]5[/latex] | [latex]10[/latex] | [latex]15[/latex] | [latex]20[/latex] | [latex]25[/latex] | [latex]30[/latex] | [latex]35[/latex] | [latex]40[/latex] | [latex]45[/latex] | [latex]50[/latex] | [latex]55[/latex] | [latex]60[/latex] |
[latex]\text{Multiples of }6[/latex] | [latex]6[/latex] | [latex]12[/latex] | [latex]18[/latex] | [latex]24[/latex] | [latex]30[/latex] | [latex]36[/latex] | [latex]42[/latex] | [latex]48[/latex] | [latex]54[/latex] | [latex]60[/latex] | [latex]66[/latex] | [latex]72[/latex] |
[latex]\text{Multiples of }7[/latex] | [latex]7[/latex] | [latex]14[/latex] | [latex]21[/latex] | [latex]28[/latex] | [latex]35[/latex] | [latex]42[/latex] | [latex]49[/latex] | [latex]56[/latex] | [latex]63[/latex] | [latex]70[/latex] | [latex]77[/latex] | [latex]84[/latex] |
[latex]\text{Multiples of }8[/latex] | [latex]8[/latex] | [latex]16[/latex] | [latex]24[/latex] | [latex]32[/latex] | [latex]40[/latex] | [latex]48[/latex] | [latex]56[/latex] | [latex]64[/latex] | [latex]72[/latex] | [latex]80[/latex] | [latex]88[/latex] | [latex]96[/latex] |
[latex]\text{Multiples of }9[/latex] | [latex]9[/latex] | [latex]18[/latex] | [latex]27[/latex] | [latex]36[/latex] | [latex]45[/latex] | [latex]54[/latex] | [latex]63[/latex] | [latex]72[/latex] | [latex]81[/latex] | [latex]90[/latex] | [latex]99[/latex] | [latex]108[/latex] |
Multiple of a Number
A number is a multiple of [latex]n[/latex] if it is the product of a counting number and [latex]n[/latex].example
Determine whether each of the following is a multiple of [latex]2\text{:}[/latex]- [latex]489[/latex]
- [latex]3,714[/latex]
1. | |
Is [latex]489[/latex] a multiple of [latex]2[/latex]? | |
Is the last digit [latex]0, 2, 4, 6, or 8[/latex]? | No. |
[latex]489[/latex] is not a multiple of [latex]2[/latex]. |
2. | |
Is [latex]3,714[/latex]a multiple of [latex]2[/latex]? | |
Is the last digit [latex]0, 2, 4, 6, or 8[/latex]? | Yes. |
[latex]3,714[/latex] is a multiple of [latex]2[/latex]. |
try it
#145413example
Determine whether each of the following is a multiple of [latex]10\text{:}[/latex]- [latex]425[/latex]
- [latex]350[/latex]
Answer: Solution:
1. | |
Is [latex]425[/latex] a multiple of [latex]10[/latex]? | |
Is the last digit [latex]0[/latex]? | No. |
[latex]425[/latex] is not a multiple of [latex]10[/latex]. |
2. | |
Is [latex]350[/latex] a multiple of [latex]10[/latex]? | |
Is the last digit [latex]0[/latex]? | Yes. |
[latex]350[/latex] is a multiple of [latex]10[/latex]. |
try it
#145418Use Common Divisibility Tests
Another way to say that [latex]375[/latex] is a multiple of [latex]5[/latex] is to say that [latex]375[/latex] is divisible by [latex]5[/latex]. In fact, [latex]375\div 5[/latex] is [latex]75[/latex], so [latex]375[/latex] is [latex]5\cdot 75[/latex]. Notice in the last example that [latex]10,519[/latex] is not a multiple [latex]3[/latex]. When we divided [latex]10,519[/latex] by [latex]3[/latex] we did not get a counting number, so [latex]10,519[/latex] is not divisible by [latex]3[/latex].Divisibility
If a number [latex]m[/latex] is a multiple of [latex]n[/latex], then we say that [latex]m[/latex] is divisible by [latex]n[/latex].Divisibility Tests | |
---|---|
A number is divisible by | |
[latex]2[/latex] | if the last digit is [latex]0,2,4,6,\text{or }8[/latex] |
[latex]3[/latex] | if the sum of the digits is divisible by [latex]3[/latex] |
[latex]5[/latex] | if the last digit is [latex]5[/latex] or [latex]0[/latex] |
[latex]6[/latex] | if divisible by both [latex]2[/latex] and [latex]3[/latex] |
[latex]10[/latex] | if the last digit is [latex]0[/latex] |
example
Determine whether [latex]1,290[/latex] is divisible by [latex]2,3,5,\text{and }10[/latex].Answer: Solution: The table below applies the divisibility tests to [latex]1,290[/latex]. In the far right column, we check the results of the divisibility tests by seeing if the quotient is a whole number.
Divisible by…? | Test | Divisible? | Check |
---|---|---|---|
[latex]2[/latex] | Is last digit [latex]0,2,4,6,\text{or }8?[/latex] Yes. | yes | [latex]1290\div 2=645[/latex] |
[latex]3[/latex] | [latex]\text{Is sum of digits divisible by }3?[/latex] [latex]1+2+9+0=12[/latex] Yes. | yes | [latex]1290\div 3=430[/latex] |
[latex]5[/latex] | Is last digit [latex]5[/latex] or [latex]0?[/latex] Yes. | yes | [latex]1290\div 5=258[/latex] |
[latex]10[/latex] | Is last digit [latex]0?[/latex] Yes. | yes | [latex]1290\div 10=129[/latex] |
try it
#145433example
Determine whether [latex]5,625[/latex] is divisible by [latex]2,3,5,\text{and }10[/latex].Answer: Solution: The table below applies the divisibility tests to [latex]5,625[/latex] and tests the results by finding the quotients.
Divisible by…? | Test | Divisible? | Check |
---|---|---|---|
[latex]2[/latex] | Is last digit [latex]0,2,4,6,\text{or }8?[/latex] No. | no | [latex]5625\div 2=2812.5[/latex] |
[latex]3[/latex] | [latex]\text{Is sum of digits divisible by }3?[/latex] [latex]5+6+2+5=18[/latex] Yes. | yes | [latex]5625\div 3=1875[/latex] |
[latex]5[/latex] | Is last digit is [latex]5[/latex] or [latex]0?[/latex] Yes. | yes | [latex]5625\div 5=1125[/latex] |
[latex]10[/latex] | Is last digit [latex]0?[/latex] No. | no | [latex]5625\div 10=562.5[/latex] |
try it
[ohm_question]145433[/ohm_question]Licenses & Attributions
CC licensed content, Original
- Question ID 145433, 145363, 145413, 145417, 145418. Authored by: Lumen Learnig. License: CC BY: Attribution. License terms: IMathAS Community License.
CC licensed content, Shared previously
- Determine Multiples of a Given Number. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Divisibility Rules. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].