Consider the following numbers
72 and 124
First find the HCF of above numbers.
72 = 2 × 2 × 2 × 3 × 3
⇒ 2³ × 3²
124 = 2 × 2 × 31
⇒ 2² × 31
To find the HCF of these numbers, take the least power of each common factor and find the product.
Here 2 is the only common factor and least power of which is 2.
So, we have
HCF(72 and 124) = 4
Now we need to express HCF = 4 as a linear combination of 72 and 124.
That is,
4 = 72a + 124b, where a and b are integers.
Use hit and trial method.
Take a = -10 and b = 6
72(-10) + 124(6)
⇒ -720 + 744 = 24, which is not equal to 4.
So, take a = -12 and b =7
72(-12) + 124(7)
⇒ - 864 + 868 = 4
So, the required linear combination is
HCF(72 and 124) = 4 = 72(-12) + 124(7)
