Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively

Hint: We know that \[ \\ $ 65 is completely divisible by the required number. Similarly, $125 - 8 = 117$ is completely divisible by the required number. Now, the required number is the HCF of 65 and 117. Write the number 65 as the product of its primes. $117 = 3 \times 3 \times 13$ Therefore, the HCF is 13 Thus, the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively is 13. Note: We can also calculate the HCF by long division method or factor tree method. HCF of numbers gives the largest number that divides all the given numbers.

Given that the number leaves a remainder 5 when it divides 60, and a remainder 8 when it divides 125. Thus, this number must divide 70-5 = 65 and 125 - 8 = 117. Now, the required number = HCF of 65, 117 [for the largest number] For this, 117 = 65 × 1 + 52 [ ∴ d i v i d e n d = d i v i s o r × q u o t i e n t + r e m a i n d e r ] ⇒ 65 = 52 × 1 + 13 ⇒ 52 = 13 × 4 + 0 ⇒ H C F = 13 Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8. The answer is A.

Given that the largest number when divides 248 and 1032, the remainder is 8 in each case.248 - 8 = 240 and 1032 - 8 = 1024 are completely divisible by the required number.Therefore, it is the HCF of 240 and 1024.Prime factorization of 240 = 2 * 2 * 2 * 2 * 3 * 5Prime factorization of 1024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2.HCF(240,1024) = 2 * 2 * 2 * 2 = 16.Therefore the largest number which divides 248 and 1032 leaving remainder 8 in each case = 16. Solution: To solve this problem, we need to find the highest common factor (HCF) of the numbers obtained by subtracting 8 from 248 and 1032, respectively. Step 1: Subtract 8 from 248 and 1032 248 - 8 = 240 1032 - 8 = 1024 Step 2: Find the HCF of 240 and 1024 To find the HCF of 240 and 1024, we can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and finding the remainder. Then we divide the smaller number by the remainder and find another remainder. We repeat this process until the remainder becomes zero. The last non-zero remainder is the HCF of the two numbers. We can write this process as follows: 1024 = 4 × 240 + 64 240 = 3 × 64 + 48 64 = 1 × 48 + 16 48 = 3 × 16 + 0 Therefore, the HCF of 240 and 1024 is 16. Step 3: Add the common remainder to the HCF Since we subtracted 8 from both numbers, we need to add 8 to the HCF to obtain the final answer. 16 + 8 = 24 Therefore, the largest number that divides 248 and 1032 leaving a remainder of 8 in each case is 24. Final Answer: 24 Q...

Solution: Concept- That number would be 13. Finding the number with the highest common factor after subtracting the remainder from the provided numbers yields the largest number. That provides us with the highest total. Because it was indicated before that the number divides the supplied number and leaves a residual, we must subtract the remainder in order to obtain the number that can be divided by the biggest number. Let's start with the number 70. It was stated that when 70 is divided by the largest number, 5 is left behind. The leftover is 8 when the number 125 is divided by the largest number. Consider 70 once more. The largest number divides 70 and leaves 5 as the remainder, thus we must deduct 5 from 70. 70 - 5 = 65 . Now, when we write the factors for 65 , we obtain 65 = 13 × 5 . The largest number divides 125 and leaves 8 as the remainder, thus we must deduct 8 from 125. 125 - 8 = 117 . Now that we have written the factors for 117 , we have 117 = 3 × 3 × 13 . We must determine H.C.F., the largest number that divides the two numbers (Highest common factor) . 65 = 13 × 5 117 = 3 × 3 × 13 . G . C . F of 70 and 125 is 13 Hence, the correct option is 13 .

Given: The largest number which divides 70 and 125 leaving remainders 5 and 8 respectively Concept Used: First subtract the remainder from the numbers and write down their factors Calculation: Here, On subtracting remainder 5 from 70 = 70 - 5 = 65 On subtracting remainder 8 from 125 = 125 - 8 = 117 ∴ Factors of 65 = 13× 5 Factors of 117 = 13× 3 × 3 ∴ The highest common factor of the numbers 65 & 117 is 13 ∴ 13 is the largest number which divides 70 & 125 leaving remainder 5 & 8 respectively. Shortcut TrickOption Method :We can see that out of the given 4 options, 2 options have a larger divisor (325,875) than the dividend (70,125). This condition will never result in reminder(5,8) . In the remaining 2 options, when the divisor is 36 and the dividend is 70, then the reminder will be 34. Finally, we have only one option 13 left.. The Navodaya Vidyalaya Samiti (NVS) has announced the final result for the recruitment of Trained Graduate Teachers (TGT) for the 2022 cycle. Candidates who had appeared for the NVS TGT recruitment can now check the final result. The Navodaya Vidyalaya Samiti (NVS) released a notification for the recruitment at the post of

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is a. 13 b. 65 c. 875 d. 1750 Solution: Given, 5 and 8 are the remainder of 70 and 125. Subtracting these remainders from the given numbers, we get (70 - 5) = 65, (125 - 8) = 117 Which are divisible by the required number. Required number = HCF of 65 and 117. 117 = 65 × 1 + 52 65 = 52 × 1 + 13 52 = 13 × 4 + 0 HCF (65, 117) = 13 Therefore, 13 is the largest number ✦ Try This: What is the HCF of 4052 and 12576 ☛ Also Check: NCERT Exemplar Class 10 Maths Exercise 1.1 Problem 5 The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is a. 13, b. 65 c. 875, d. 1750 Summary: The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 13 ☛ Related Questions: • • •

Step -1: Subtracting remainders from the given numbers. As 7 0 leaves remainder 5 when divided by the required largest number. ⇒ The largest number will completely divide 7 0 − 5 = 6 5 . And 1 2 5 leaves remainder 8 when divided by the required largest number. ⇒ The largest number will also completely divide 1 2 5 − 8 = 1 1 7 . Step -2: Finding H.C.F. of 65 and 117. Factors of 6 5 = 5 × 1 3 Factors of 1 1 7 = 3 × 3 × 1 3 ∴ The H.C.F. of 6 5 and 1 1 7 is 1 3 . Hence, 1 3 is the required largest number. Hence, correct option is A.