If remainder of (5+1)(5+3)(5+4) is a natural number ,then find it.
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5
Pls answers asap
Answers
Answer:
Remainder is 2
Step-by-step explanation:
What will be the remainder of (5m+1)(5m+3)(5m+4)/5?
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[math]\left( {5m + 1} \right) \equiv 1\bmod \left( 5 \right)[/math]
[math]\left( {5m + 3} \right) \equiv 3\bmod \left( 5 \right)[/math]
[math]\left( {5m + 4} \right) \equiv 4\bmod \left( 5 \right)[/math]
[math] \Rightarrow \left( {5m + 1} \right)\left( {5m + 3} \right)\left( {5m + 4} \right) \equiv \left( 1 \right)\left( 3 \right)\left( 4 \right)\bmod \left( 5 \right)[/math]
[math] \Rightarrow \left( {5m + 1} \right)\left( {5m + 3} \right)\left( {5m + 4} \right) \equiv 12\bmod \left( 5 \right)[/math]
[math] \Rightarrow \left( {5m + 1} \right)\left( {5m + 3} \right)\left( {5m + 4} \right) \equiv 2\bmod \left( 5 \right)[/math]
What is the remainder of (-11) /4?
How will the remainder be 5 or 7?
What is -1/4%(3+5) =?
What is 1+2+3+4+5*1*2*3*4*5-1-2-3-4-5/1/2/3/4/5?
What is the remainder of 3/6?
All factors of Numerators are not divisible by 5 so each one produce a remainder.
Get all the remainders. i.e. 1,3and 4.
Multiply them to get an equivalent remainder. i.e. 12.
But 12 is more than 5.
To get final remainder Divide 12 by 5. We get 2 as remainer.
So Answer is 2.
Also, you can cross verify by assuming any value of m.
If m=1
6*8*9= 432. 432/5 gives 2 as remainder.
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(5m+1)*(5m+3)*(5m+4) is
= (25m^2+20m+3)*(5m+4), which is
= 125m^3+200m^2+95m+12, which is
= 125m^3+200m^2+95m+10+2, which is
= 5*(25m^3+40m^2+19m+2) + 2 /* Taking 5 common */
Thus you can see, the remainder comes to 2 as the other portion has 5 as the factor.
What is the remainder of (-11) /4?
How will the remainder be 5 or 7?
What is -1/4%(3+5) =?
What is 1+2+3+4+5*1*2*3*4*5-1-2-3-4-5/1/2/3/4/5?
What is the remainder of 3/6?
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