What is the remainder when 30 is divided by 4?
One approach:
1. Break the dividend 30 into factors: 30 = 5*6
2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2
3. Multiple the resulting remainders: 1*2 = 2
Step 3 indicates that 30 divided by 4 will yield a remainder of 2.
This approach can be applied to any problem that asks for the remainder when a large integer is divided by a divisor.
Repeat the 3 steps until the value yielded by Step 3 is less than the divisor.
Quote:
What is the remainder when 1044*1047*1050*1053 is divided by 33?
A. 3
B. 27
C. 30
D. 21
E. 18
Since 1044 has a digit sum that is a multiple of 3 (1+0+4+4=9), 1044 is divisible by 3:
1044 = 3*348
Since 1047 is 3 more than 1044, 1047 = 3*348 + 3 = 3(348+1) = 3*349
By extension:
1050 = 3*350
1053 = 3*351
Thus:
1044*1047*1050*1053 = (3*348)(3*349)(3*350)(3*351) =
81*348*349*350*351Dividing 33 into each of the five factors in blue and multiplying the resulting remainders, we get:
15*18*19*20*21
18*20 = 360
19*21 = (20-1)(20+1) = 20²-1² = 400-1 = 399
Thus:
15*18*19*20*21 =
15*360*399Dividing 33 into each of the 3 factors in red and multiplying the resulting remainders, we get:
15*30*3
15*30*3 = 1350
Dividing 33 into 1350, we get:
40 R
30The value in green is less than the divisor (33) and thus is the desired remainder.
.
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