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Value of 327 in the mod 7 system?

Anonymous

∙ 15y ago

Updated: 4/28/2022

327 Ξ 645 (mod 7)

(6 x 72) + (4 x 7) + 5 = 294 + 28 + 5 = 327

Wiki User

∙ 15y ago

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Q: Value of 327 in the mod 7 system?

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What is the value of 7 in 327?

7 units (ones).

What is the place value of seven in 327 000?

If you mean: 327,000 then the place value of 7 is 7,000 which is seven thousand

What is remainder when 5 to the power of 30 is divided by 7?

Look at the powers of 5 mod 7: 5¹ mod 7 = 5 5² mod 7 = 5 × (5¹ mod 7) mod 7 = (5 × 5) mode 7 = 25 mod 7 = 4 5³ mod 7 = 5 × (5² mod 7) mod 7 = (5 × 4) mod 7 = 20 mod 7 = 6 5⁴ mod 7 = 5 × (5³ mod 7) mod 7 = (5 × 6) mod 7 = 30 mod 7 = 2 5⁵ mod 7 = 5 × (5⁴ mod 7) mod 7 = (5 × 2) mod 7 = 10 mod 7 = 3 5⁶ mod 7 = 5 × (5⁵ mod 7) mod 7 = (5 × 3) mod 7 = 15 mod 7 = 1 5⁷ mod 7 = 5 × (5⁶ mod 7) mod 7 = (5 × 1) mod 7 = 5 mod 7 = 5 At this point, it is obvious that the remainders will repeat the cycle {5, 4, 6, 2, 3, 1} There are 6 remainders in the cycle, so the remainder of 30 divided by 6 will tell you which remainder to use; if the remainder is 0, use the 6th element. 30 ÷ 6 = 5 r 0 →use the 6th element which is 1, so 5³⁰ ÷ 7 will have a remainder of 1. 1 &equiv; 5³⁰ mod 7.

Why does -24 mod 7 equal 4 but 24 mod 7 equal 3?

The modulus of a number relative to a base is the positive remainder when itis divided by that base. So -24 mod 7 = (-28 + 4) mod 7 = -28 mod 7 + 4 mod 7 = 4 mod 7 = 4while 24 mod 7 = (21 + 3) mod 7 = 21 mod 7 + 3 mod 7 = 3 mod 7 = 3.

How many times does 40 go into 327?

327 ÷ 40 = 8 with remainder 7 OR 8.175 times.

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Related Questions

Find the value of 327 in the mod 7 system?

the answer is 5

How do you solve the problem of finding the value of 327 in the mod 7 system?

5Divide 327 by seven, but stop before you get decimals. 327/7 = 46 with remainder 5. 327mod7 = 5If you are doing this on a regular calculator, put in 327/7. You will get 46.71428.... Now subtract 46; this will leave 0.71248... Multiply by 7 and you will have the remainder, 5.

What is the value of 7 in 327?

7 units (ones).

What is the place value of seven in 327 000?

If you mean: 327,000 then the place value of 7 is 7,000 which is seven thousand

What is remainder when 5 to the power of 30 is divided by 7?

Look at the powers of 5 mod 7: 5¹ mod 7 = 5 5² mod 7 = 5 × (5¹ mod 7) mod 7 = (5 × 5) mode 7 = 25 mod 7 = 4 5³ mod 7 = 5 × (5² mod 7) mod 7 = (5 × 4) mod 7 = 20 mod 7 = 6 5⁴ mod 7 = 5 × (5³ mod 7) mod 7 = (5 × 6) mod 7 = 30 mod 7 = 2 5⁵ mod 7 = 5 × (5⁴ mod 7) mod 7 = (5 × 2) mod 7 = 10 mod 7 = 3 5⁶ mod 7 = 5 × (5⁵ mod 7) mod 7 = (5 × 3) mod 7 = 15 mod 7 = 1 5⁷ mod 7 = 5 × (5⁶ mod 7) mod 7 = (5 × 1) mod 7 = 5 mod 7 = 5 At this point, it is obvious that the remainders will repeat the cycle {5, 4, 6, 2, 3, 1} There are 6 remainders in the cycle, so the remainder of 30 divided by 6 will tell you which remainder to use; if the remainder is 0, use the 6th element. 30 ÷ 6 = 5 r 0 →use the 6th element which is 1, so 5³⁰ ÷ 7 will have a remainder of 1. 1 &equiv; 5³⁰ mod 7.

Why does -24 mod 7 equal 4 but 24 mod 7 equal 3?

The modulus of a number relative to a base is the positive remainder when itis divided by that base. So -24 mod 7 = (-28 + 4) mod 7 = -28 mod 7 + 4 mod 7 = 4 mod 7 = 4while 24 mod 7 = (21 + 3) mod 7 = 21 mod 7 + 3 mod 7 = 3 mod 7 = 3.

Sw mod 10-7 value?

50-400 USD depending on specifics

What is the value of a walther mod 7 good to border line excl. cond.?

Requires professional appraisal

Is garrys mod compatible with windows 7?

Yes, Garry's Mod is compatible with Windows 7. Afforablekey. com is one of the best websites to buy Garry's Mod for your Windows 7 operating system. To celebrate Mother's Day, they have a limited-time offer on their best sellers--up to 30% discount on your purchase when you use coupon code HAPPYMD.

How many times does 40 go into 327?

327 ÷ 40 = 8 with remainder 7 OR 8.175 times.

What is the remainder when the product of 100 5's are divided by 7?

The remainder is 2. Knowing how to do modular arithmetic makes the problem much easier to solve. We say a number x has a value of k "mod" 7 if dividing x by 7 leaves a remainder of k. Multiples of 7 are equal to 0 mod 7 (they leave no remainder), and 32 is equal to 4 mod 7, because 32 / 7 = 4 remainder 4. The product of 100 5s is equal to 5 to the 100th power, or 5^100 in shorthand. Let us look at what the first few powers of 5 are equal to mod 7: 5^1 = 5 = 5 mod 7 5^2 = 25 = 4 mod 7 5^3 = 125 = 6 mod 7 5^4 = 625 = 2 mod 7 5^5 = 3125 = 3 mod 7 5^6 = 15625 = 1 mod 7 5^7 = 78125 = 5 mod 7 5^8 = 390625 = 4 mod 7 It looks as if we might have a repeating pattern, and indeed the next few powers of 5 are equal to 6, 2, and 3, confirming that 5^k = 5^(k-6) mod 7. This means that 5^100 has the same remainder after dividing by 7 as 5^94, which has the same remainder as 5^88, etc. etc. until we reach 5^4, which leaves a remainder of 2. Therefore by induction 5^100 leaves a remainder of 2. Hope this all makes sense.

Is 327 divisible by 3?

To determine if 327 is divisible by 3, we need to sum its digits. 3 + 2 + 7 = 12. Since 12 is divisible by 3, 327 is also divisible by 3. Therefore, yes, 327 is divisible by 3.

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