Question

Greatest number which divides 240 and 360 leaving remainder 2 and 3

Answer 1

the greatest number which divides 240 and 360 leaving remainder 2 and 3 is 120
240/120=2
360/120=3

Answer 2

Answer:

Required greatest number is 119.

Step-by-step explanation:

Given, a greatest number which divides 240 and 360 leaving remainder 2 and 3.

So, the greatest number which divides (240-2) = 238 and (360-3) = 357 without any remainder.

We are factorising 238 and 357,

$238 = 2 \times 7 \times 17 \\ 357 =3 \times 7 \times 17$

So, Greatest common divisor of 238 and 357 is (7×17) = 119

So, required Greatest number is 119.

Know more about GCD:

The greatest common divisor (GCD) of two or more numbers is the number of the greatest common factor that exactly divides them. It is also called the highest common factor (HCF). For example, the greatest common factor of 15 and 10 is 5 because both numbers are divisible by 5.

15/5 = 3

10/5 = 2

If a and b are two numbers, the greatest common divisor of both numbers is denoted gcd(a, b). To find the gcd of numbers, we need to list all the factors of the numbers and find the greatest common factor.

Suppose 4, 8 and 16 are three numbers. Then the factors of 4, 8 and 16 are:

4 → 1,2,4

8 → 1,2,4,8

16 → 1,2,4,8,16

Therefore, we can conclude that 4 is the greatest common factor of all three numbers.

How to find the greatest common divisor

Before we get into finding the greatest common factor of numbers, let's understand what is a factor and what are common factors?

What are the factors?

The factors of a number divide the prime equally. For example, if 8 is a factor of 64, then 8 can divide 64 into 8 equal parts.

What are the most common factors?

If a factor of a number is a factor of another number, it is said to be a common factor of the two numbers. For example, 2 is a factor of 4 and 8, so 2 is a common factor.

GCD is the greatest common factor of two or more numbers. The factor that is the highest among the numbers.

Methods of finding GCD:

• There are several methods for finding the greatest common divisor of two given numbers.
• Prime factorization method
• Long division method
• Euclidean division algorithm

Know more about GCD,

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