the sum of two positive integers $a$ and $b$ is $1001$. what is the largest possible value of $\gcd(a,b)$?

Sagot :

The two integers 143m, 143n  = a, b  have only the factor of 143 in common.....and it is the g c d of both given , two positive integers of a and b is = 1001 factors 0f 1001is = 7 x 11 x 13 So.....143 is the greatest proper divisor of 1001.This means, that we have  143( m + n)  = 143m + 143m = a + b = 1001,  where ( m + n) = 7  and,

 m + n are two positive integers whose sum = 7,

they are relatively prime to each other.

Therefore, these two integer 143m, 143n  = a, b  have only the factor of 143 in common.....and it is the g c d of both

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integers come in three types: Zero (0) Positive Integers (Natural numbers) Negative Integers (Additive inverse of Natural Numbers)

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes: Positive Numbers: A number is positive if it is greater than zero.

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