Highest Common Factor of 242, 7781 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 242, 7781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 242, 7781 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 242, 7781 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 242, 7781 is 1.
HCF(242, 7781) = 1
HCF of 242, 7781 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 242, 7781 is 1.
Highest Common Factor of 242,7781 is 1
Step 1: Since 7781 > 242, we apply the division lemma to 7781 and 242, to get
7781 = 242 x 32 + 37
Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 37 and 242, to get
242 = 37 x 6 + 20
Step 3: We consider the new divisor 37 and the new remainder 20, and apply the division lemma to get
37 = 20 x 1 + 17
We consider the new divisor 20 and the new remainder 17,and apply the division lemma to get
20 = 17 x 1 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 242 and 7781 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(20,17) = HCF(37,20) = HCF(242,37) = HCF(7781,242) .
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Frequently Asked Questions on HCF of 242, 7781 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 242, 7781?
Answer: HCF of 242, 7781 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 242, 7781 using Euclid's Algorithm?
Answer: For arbitrary numbers 242, 7781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.