Find the largest two digit number that divides 673 and 865 leaving remainder 1 in each

In order to find the greatest number which divides 285 and 1249 leaving remainders 9 and 7

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• Solve for the HCF to get the required number,Finding factors for the first number, 673-1=672 (As the remainder is 1.)Factorize 672⇒672=2×2×2×2×2×3×7Finding factors for the second number,865-1=864(Remainder is 1)Factorize 864⇒864=2×2×2×2×2×3×3×3The HCF of 672 and 864 isHC F(672,864)=2×2×2×2×2 ×3⇒HCF(672,864)=96Hence, the largest two-digit number that divides 673 and 865 by leaving the remainder 1 in each is 96.
• The correct option is A5To find the largest number that divides 679 and 599 leaving remainder 4 in each case We need to find the largest number that divides 679-4=675 and 599-4 = 595 i.e the the HCF of 675 and 595 HCF(675,595) =5
• What is the largest number that divides 445 572 and 699 and leaves remainder of 4/5 and 6 respectively?
• What is the greatest number that will divide 6844 and 6123 and leave remainder 4 and 3 respectively?
• What is the largest number which divides 129 and 545 leaving remainder 3 and 5 respectively?
• What is the largest number which divides 70 and 123 leaving remainder 5 and 8 respectively?

We get

285 – 9 = 276

1249 – 7 = 1242

So the required number = HCF of 276 and 1242

By resolving the required number into prime factors

we get

276 = 2 × 2 × 3 × 23

1242 = 2 × 3 × 3 × 3 × 23

So the HCF of 276 and 1242 = 2 × 3 × 23 = 138

Therefore, the greatest number which divides 285 and 1249 leaving remainders 9 and 7 is 138.

Answer

Verified

Hint: Subtracting the remainder from the given numbers and finding the highest common factor gives the greatest number. That gives us the largest number. We have to subtract because above it was mentioned that the number divides the given number and leaves a remainder that means remainder is subtracted to get the number which is divisible by the largest number.Complete step-by-step solution -
 Let us consider the number 70 first,
Here it was given that 70 when divided by the greatest number leaves the remainder as 5.
Similarly the number 125 when divided by the greatest number leaves the remainder as 8.
Now Considering 70 again.
The greatest number divides 70 and leaves the remainder as 5, that means we have to subtract 5 from 70.
\[70-5=65\].
Now writing the factors for 65 we get,
\[65=13\times 5\]
The greatest number divides 125 and leaves the remainder as 8, that means we have to subtract 8 from 125.
\[125-8=117\].
Now writing the factors for 117 we get,
\[117=3\times 3\times 13\].
To find the greatest number that divides the 2 numbers, we have to find H.C.F (Highest common factor).
\[65=13\times 5\].
\[117=3\times 3\times 13\].
H.C.F of 70 and 125 is \[13\].
Therefore the greatest number that divides 70 and 125 by leaving remainder 5 and 8 is 13.

Note: This is a direct problem with finding the greatest number by writing the factors. The basic step here is to subtract the remainder and then find the greatest number. Highest common factor gives the greatest number that divides the given number.

Find The Largest 2 Digit Number That Divides 673 And 865 Leaving Remainder 1 In Each Maths Q&A

Solution

Solve for the HCF to get the required number,Finding factors for the first number, 673-1=672 (As the remainder is 1.)Factorize 672⇒672=2×2×2×2×2×3×7Finding factors for the second number,865-1=864(Remainder is 1)Factorize 864⇒864=2×2×2×2×2×3×3×3The HCF of 672 and 864 isHC F(672,864)=2×2×2×2×2 ×3⇒HCF(672,864)=96Hence, the largest two-digit number that divides 673 and 865 by leaving the remainder 1 in each is 96.

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Solution

The correct option is A5To find the largest number that divides 679 and 599 leaving remainder 4 in each case We need to find the largest number that divides 679-4=675 and 599-4 = 595 i.e the the HCF of 675 and 595 HCF(675,595) =5

What is the largest number that divides 445 572 and 699 and leaves remainder of 4/5 and 6 respectively?

Answer: 63 is the largest divisor that will give the desired remainders. Q. Find the greatest number that will divide 445, 572 and 699, leaving remainders 4, 5, 6 respectively.

What is the greatest number that will divide 6844 and 6123 and leave remainder 4 and 3 respectively?

We need the highest number that divides 6844 and 6123 and leave remainders 4 and 3 respectively. HCF = 2 × 2 × 2 × 3 × 3 × 5 = 360. Therefore, the number is 360.

What is the largest number which divides 129 and 545 leaving remainder 3 and 5 respectively?

Consider HCF be x. In order to make 129 and 545 completely divisible by x, we need to deduct the remainder 3 and 5 from the cases. ∴ largest number which divides 126 and 540 leaving remainder 3 and 5 in case is 18.

What is the largest number which divides 70 and 123 leaving remainder 5 and 8 respectively?

Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8 respectively.

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