Question

Find the greatest number which divides 70 and 125 leaving no remainder.

Answer 1

Answer:

Since, 5 and 8 are remainders of 70 and 125 respectively.Thus, after subtracting these remainders from the numbers, we have the number 65 = (70 - 5), 117 = (125 - 8), which is divisible by the required number. Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

Step-by-step explanation:

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Answer 2

Answer:

The Greatest Number which divides 70 and 125 leaving no remainder is 5.

Step-by-step explanation:

Given :

The two numbers = 70 and 125

Condition = There should be no remainder when both the numbers are divided

To find :

Greatest number which divides 70 and 125 leaving no remainder

Solution :

To get the greatest number, we simply need to find the Highest Common Factor (HCF) which is also know as Greatest Common Divisor (GCD) of the two given numbers.

HCF by Prime Factorisation Method -

★ $\textsf{\underline{\underline{Prime Factorisation of 70}}}$

$\begin{array}{r|l} 2 & 70 \\\cline{1-2} 5 & 35 \\\cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Prime Factorisation of 125}}}$

$\begin{array}{r|l} 5 & 125 \\\cline{1-2} 5 & 25 \\\cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

70 = 2 × 5 × 7

125 = 5 × 5 × 5

→ HCF = 5

$\therefore$ The Greatest Number which divides 70 and 125 leaving no remainder is 5.

$\rule{300}{1.5}$

Verification :-

Refer the attachment for complete division.

$\implies$ 70 ÷ 5

$\implies$ 14

$\implies$ 125 ÷ 5

$\implies$ 25