Kanta is trying to find the highest common factor of 42 and 455 using Euclid's division algorithm (EDA). In her third step, she gets the divisor of 7. Find the remainder at the end of the 3rd step.
Answers
Step-by-step explanation:
42)455(10
42
...................
35
0
........................
7)35(5
35
.....................
0
therefore, 455=42(10)+35
42=35(1)+7
35=7(5)+0
HCF = 7
Answer:
The remainder at the end of the third step = 0
Step-by-step explanation:
Given,
Two numbers 42 and 455
To find,
The remainder at the end of 3rd step
Recall the theorem
Euclid's Division Lemma or Euclid division algorithm
For any two positive integers a and b, we can find two unique integers p and r such that a, b, p,r satisfies the equation,
a = bp+ r, 0≤r<b, Here 'a' is called the dividend, b is the divisor, q is the quotient and 'r' is the reminder
Step 1: Divide 455 by 42
By division lemma, we get
455 = 1×42 +35
Step 2: Divide 42 by 35
By division lemma, we get
42 = 1×35 +7
Step 3: divide 35 by 7
By division lemma, we get
35 = 5×7 + 0
∴The remainder at the end of the third step = 0
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