Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Express the HCF of 72 and 124 as a linear combination of 72 and 124

Express the HCF of 72 and 124 as a linear combination of 72 and 124

Grade:10

1 Answers

Arun
25763 Points
4 years ago
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)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free