∴ 10 x Quotient = 230 ⟹ = | 230 | = 23 |
10 |
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
∴Required remainder = 5.
Correct Quotient = 420 ? 21 = 20
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
∴373 is prime.
Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944.
The smallest 6-digit number 100000. 111) 100000 (900 999 ----- 100 --- Required number = 100000 + (111 - 100) = 100011.
But, unit digit in (74)26 = 1
∴ Unit digit in 7105 = (1 x 7) = 7
Given Exp. = | (1000)9 | = | (103)9 | = | (10)27 | = 10(27-24) = 103 = 1000 |
1024 | 1024 | 1024 |
106 x 106 - 94 x 94 | = (106)2 - (94)2 |
= (106 + 94)(106 - 94) [Ref: (a2 - b2) = (a + b)(a - b) ] | |
= (200 x 12) | |
= 2400. |
(112 x 54) = 112 x | ❨ | 10 | ❩ | 4 | = | 112 x 104 | = | 1120000 | = 70000 |
2 | 24 | 16 |
587 x 999 | = 587 x (1000 - 1) |
= 587 x 1000 - 587 x 1 | |
= 587000 - 587 | |
= 586413. |
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