Question 6 - Figure it out - Page 125, 126 - Chapter 5 Class 6 - Prime Time (Ganita Prakash)

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Question 6 Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10: 572, 2352, 5600, 6000, 77622160.From last question, we noted that If number is divisible by 8 and 10, then it is divisible by all 2, 4, 5, 8, 10 Thus, we check divisibility of all numbers by 8 and 10 only Divisibility by 10 Since number doesn’t end with 0 ∴ 572 is not divisible by 10 Divisibility by 8 Last 3 digits are 572 Since remainder is not 0 ∴ 572 is not divisible by 8 Thus, 572 is not divisible by all 2, 4, 5, 8, 10 Divisibility by 8 Last 3 digits are 352 Since remainder is 0 ∴ 2352 is divisible by 8 Since 2352 is not divisible by 10 Thus, 2352 is not divisible by all 2, 4, 5, 8, 10 Divisibility by 10 Since number ends with 0 ∴ 5600 is divisible by 10 Divisibility by 8 Last 3 digits are 600 Since remainder is 0 ∴ 2352 is divisible by 8 Since 5600 is divisible by 10 and 8 Thus, 5600 is divisible by all 2, 4, 5, 8, 10 Divisibility by 10 Since number ends with 0 ∴ 6000 is divisible by 10 Divisibility by 8 Last 3 digits are 000 And 0 is divisible by all numbers As 0/8=0 So, it is divisible by 8 ∴ 6000 is divisible by 8 Since 6000 is divisible by 10 and 8 Thus, 6000 is divisible by all 2, 4, 5, 8, 10 Divisibility by 10 Since number ends with 0 ∴ 6000 is divisible by 10 Divisibility by 8 Last 3 digits are 000 And 0 is divisible by all numbers As 0/8=0 So, it is divisible by 8 ∴ 77622160 is divisible by 8 Divisibility by 10 Since number doesn’t end with 0 ∴ 2352 is not divisible by 10 Since 77622160 is divisible by 10 and 8 Thus, 77622160 is divisible by all 2, 4, 5, 8, 10 Divisibility by 8 Last 3 digits are 160 Since remainder is 0 ∴ 77622160 is divisible by 8 Divisibility by 10 Since number ends with 0 ∴ 77622160 is divisible by 10 Since 77622160 is divisible by 10 and 8 Thus, 77622160 is divisible by all 2, 4, 5, 8, 10