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This CBSE class 10 Maths Extra Practice Question is from the chapter Real Numbers. This word problem tests your understanding of computing the value of the largest divisor that divides 3 numbers leaving 3 different remainders.

Nội dung chính

Question 5 : What is the largest number that divides 170, 220, and 420 leaving remainders 8, 4, and 15 respectively?

Target Centum in CBSE 10th Maths

Online CBSE Course
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Video Solution

NCERT Solution to Class 10 Maths

With Videos

Explanatory Answer

Given Data: The three numbers are 170, 220, and 420.

Step 1 – Decoding Given Information

Let x be the largest number that divides 170, 220, and 420 leaving reaminders of 8, 4, and 15 respectively.
Remainder of fractext170textx) is 8.
=> 170 – 8 = 162 is divisible by x.
Remainder of fractext220textx) is 4.
=> 220 – 4 = 216 is divisible by x.

Remainder of fractext420textx) is 15.
=> 420 – 15 = 405 is divisible by x.

So, we can infer that x divides 162, 216, and 405 without leaving any remainder.
Or, x is a factor of 162, 216, and 405. i.e., x is a common factor of 162, 216, and 405.
Because x is the largest such number, x is the HCF OF 162, 216 and 405.

Step 2 – Use Euclid’s Division Lemma to find the HCF of the 3 Numbers

Step 1: Apply Euclid’s Division Lemma on

216 with 162 as divisor.
216 = 162 × 1 + 54
The remainder is not zero.
Step 2: Apply Euclid’s Division Lemma on 162 with 54 as divisor.
162 = 54 × 3 + 0.
The remainder is 0.
∴ The divisor of this step, 54 is the HCF of 162 and 216.
Step 3: Find HCF of 54 and 405
Apply Euclid’s Division Lemma on 405 with 54 as divisor.
405 = 54 × 7 + 27
The remainder is not zero.
Step 4: Apply Euclid’s Division Lemma on 54 with 27 as

divisor.
54 = 27 × 2 + 0
The remainder is zero.
∴ The divisor of this step, 27 is the HCF of 54 and 405.
Hence, 27 is the HCF of 162, 216, and 405.

27 is the largest number that divides 170, 220, and 420 leaving remainders of 8, 4, and 15 respectively.

Find the Largest Number which Divides 110, 140, 170

Find the largest number which divides 110, 140, 170 leaving reminders of 2, 5, 8 respectively.

Asked by: Geeta on Dec 14, 2022.

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Find the greatest number that can exactly divide 140, 170 and 155 leaving remainder 5 in each case

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So in this question we need

to find greatest numbers that can exactly divide 1 40 1 40 1 17 1 70 and 1 55 living reminder living remainder five in each is five in each if inch kits. So that that test number will be simply cf 1 40 -5, 1 70 -5 And 155 -5. So basically here we need to find Cf 1 35. 1 35. 1 35 1 65 and 1 50. Now Frank a creation of 135 is equal to simply three youth and 2 5 27- five actually. and 165 can written as simply three Into 5- 11. That is between 11 and 1 50. Can you like written us simply two

square who’s squared? Indo three into five squared. So from here we can easily say that CIA for 1 35 1 65 150 is equal to 3 to 5 And that is close to 15 So 15 is that By which we can divide 1 40 1 71 55 living remember five in each case. So this is the final answer. I hope you like the solution. Thank you so much

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