Question

Which is the largest number that divides 185 and 167 and leaves remainder 5

Answer 1

Here is your answer

$\rule{135}{2}$

The largest number, in the question, means HCF [Highest Common Mulitple]

Firstly, we will subtract 5 from the given numbers, i.e., 185 and 167

185 = 185 - 5 = 180

167 = 167 - 5 = 162

Secondly, we will find the prime factors of the obtained numbers that were subtracted from the given numbers.

180 = 2 * 2 * 3 * 3 * 5

162 = 2 * 3 * 3 * 3 * 3

Common factors = 2 * 3 * 3

= 18

∴  The largest number that divides 185 and 167 and leaves remainder 5 = 18

Answer 2

HEY MATE HERE IS YOUR ANSWER
$\rule{135}{2}$

The largest numbers are HCF

===========================

Step 1.

Subtract 5 from both numbers

We get,

185 - 5 = 180

167 - 5 = 162

============================

Step 2.

Make their factors and common factors

Factors of 180

➡️ 180 = 2 × 2 × 3 × 3 × 5

➡️ 162 = 2 × 3 × 3 × 3 × 3

Common = 2 × 3 × 3 = 18

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Therefore, the largest number that divides 185 and 167 after minus 5 is $\huge \bold {\underline {18}}$

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