Divisibility by 24

Transcript

Divisibility by 24DIVISIBILITY RULE OF 24 Number must be divisible by BOTH 3 and 8. EXAMPLE: 12384 Divisible by 3: Yes (Sum of digits: , and 18 is divisible by 3 ). Divisible by 8: Yes (Last 3 digits 384 are divisible by 8). So, 12384 is divisible by 24.To check Divisibility of 24, we check its factors Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24 Determining divisibility by 24 by checking divisibility by 4 and by 6 does not work. For example, the number 12 is divisible by both 4 and 6, but not by 24. This is because 4 & 6 have common factors So, To check for the divisibility by 24, we can instead check for the divisibility by 3 and divisibility by 8. Let’s do some examples Is 3168 is divisible by 24? Let’s check divisibility by 3 and 8 Since 3168 is divisible by both 3 and 8 ∴ 3168 is divisible by 24 Divisibility by 3 Sum of digits = 3 + 1 + 6 + 8 = 18 Since 18 is divisible by 3 So, 3168 is divisible by 3 Divisibility by 8 Last three digits are 168. And, 168/8 = 21 So, 3168 is divisible by 8 Is 12288 is divisible by 24? Let’s check divisibility by 3 and 8 Since 12288 is divisible by both 3 and 8 ∴ 12288 is divisible by 24 Divisibility by 3 Sum of digits = 1 + 2 + 2 + 8 + 8 = 21 Since 21 is divisible by 3 So, 12288 is divisible by 3 Divisibility by 8 Last three digits are 288. And, 288/8 = 36 So, 12288 is divisible by 8 Is 3160 is divisible by 24? Let’s check divisibility by 3 and 8 Since 3160 is not divisible by both 3 and 8 ∴ 3160 not divisible by 24 Divisibility by 3 Sum of digits = 3 + 1 + 6 + 0 = 10 Since 10 is not divisible by 3 So, 3160 is not divisible by 3 Divisibility by 8 Last three digits are 160. And, 160/8 = 20 So, 3160 is divisible by 8 Is 5121 is divisible by 24? Let’s check divisibility by 3 and 8 Since 5121 is not divisible by both 3 and 8 ∴ 5121 not divisible by 24 Divisibility by 3 Sum of digits = 5 + 1 + 2 + 1 = 9 Since 9 is divisible by 3 So, 5121 is divisible by 3 Divisibility by 8 Last three digits are 121. And, 121/8 has remainder So, 5121 is not divisible by 8