Question

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

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Answer 1

Number when divides 70 and 125 leaves remainders 5 and

Number when divides 70 and 125 leaves remainders 5 and 8, then

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117then HCF of 65 and 117 is

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117then HCF of 65 and 117 is65=5×13

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117then HCF of 65 and 117 is65=5×13117=3×3×13

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117then HCF of 65 and 117 is65=5×13117=3×3×13Hence, HCF of 65 and 117 is 13.

Number when divides 70 and 125 leaves remainders 5 and 8, then70−5=65125−8=117then HCF of 65 and 117 is65=5×13117=3×3×13Hence, HCF of 65 and 117 is 13.13 is the largest number which divides 70 and 125 and leaves remainders 5 and 8.

Answer 2

Given

✭ 70 & 125 are divided by a number

✭ It gives a remainder of 5 & 8

To Find

◈ The largest number?

Solution

Concept

We shall first subtract the remainder from the given numbers and we have to find their HCF to find our final answer

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Subtracting remainder

»» 70-5 = 65

»» 125-8 = 117

Now we may use two methods to find their HCF

Method 1

We shall use the Euclid's Division Algorithm to find their HCF, which is,

A = B(Q)+R

117 > 65

➝ 117 = 65(1)+52

➝ 65 = 52(1)+13

➝ 52 = 13(4)+0

∴ HCF(65,117) is 13

Method 2

We may also use the factorisation method,

➳ 117 = 3 × 3 × 13 = 3²× 13

➳ 65 = 5 × 13

HCF of two numbers is the product of the least power of the common factors

∴ HCF(65,117) is 13

So the largest number which divides 70 and 125 leaving remainders 5 and 8 is 13

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