The factors of the given numbers include several instances of 4, 8, 11, and 12. Specifically, 180 has 4 and 12 as factors; 275 has 11; 360 has 4, 8, and 12; 688 has 4 and 8; and 440 has 4, 8, and 11. Thus, the factors you can encircle are: 4 and 12 for 180, 11 for 275, 4, 8, and 12 for 360, 4 and 8 for 688, and 4, 8, and 11 for 440.
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To determine if 4, 8, 11, and 12 are factors of the given numbers, we need to divide each number by these potential factors. A number is a factor if it divides evenly into the number, meaning there is no remainder.
180 :
4 : 180 divided by 4 equals 45, so 4 is a factor.
8 : 180 divided by 8 equals 22.5, so 8 is not a factor.
11 : 180 divided by 11 equals approximately 16.36, so 11 is not a factor.
12 : 180 divided by 12 equals 15, so 12 is a factor.
275 :
4 : 275 divided by 4 equals 68.75, so 4 is not a factor.
8 : 275 divided by 8 equals 34.375, so 8 is not a factor.
11 : 275 divided by 11 equals 25, so 11 is a factor.
12 : 275 divided by 12 equals approximately 22.92, so 12 is not a factor.
360 :
4 : 360 divided by 4 equals 90, so 4 is a factor.
8 : 360 divided by 8 equals 45, so 8 is a factor.
11 : 360 divided by 11 equals approximately 32.73, so 11 is not a factor.
12 : 360 divided by 12 equals 30, so 12 is a factor.
688 :
4 : 688 divided by 4 equals 172, so 4 is a factor.
8 : 688 divided by 8 equals 86, so 8 is a factor.
11 : 688 divided by 11 equals approximately 62.55, so 11 is not a factor.
12 : 688 divided by 12 equals approximately 57.33, so 12 is not a factor.
440 :
4 : 440 divided by 4 equals 110, so 4 is a factor.
8 : 440 divided by 8 equals 55, so 8 is a factor.
11 : 440 divided by 11 equals 40, so 11 is a factor.
12 : 440 divided by 12 equals approximately 36.67, so 12 is not a factor.