Subject
Quantitative Aptitude
Topic
Number
What is the largest number which when divides 64, 78 and 115 leaves 4, 6 and 7 as remainders, respectively?
What is the largest number which when divides 64, 78 and 115 leaves 4, 6 and 7 as remainders, respectively?
ক)
24খ)
36গ)
48ঘ)
12ঙ)
170Explanation
Let the number to be found is x. When 64 is divided by x, remainder is 4 ⇒ (64 – 4 = 60) is completely divisible by x. Similarly, 78 is divided by x, the remainder is 6 ⇒ (78 – 6 = 72) is completely divisible by x. Also, when 115 is divided by x, remainder is 7 ⇒ (115 – 7 = 108) is completely divisible by x. ∵x is the largest number that divides 60, 72 and 108, x must be the HCF of 60, 72 and 108. 60 = 2 × 2 × 3 × 5 72 = 2 × 2 × 2 × 3 × 3 108 = 2 × 2 × 3 × 3 × 3 ∴ HCF = 2 × 2 × 3= 12 ∴ required number = 12Related questions
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