Highest Common Factor of 7442, 2122 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 7442, 2122 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7442, 2122 is 2 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 7442, 2122 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 7442, 2122 is 2.
HCF(7442, 2122) = 2
HCF of 7442, 2122 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7442, 2122 is 2.
Highest Common Factor of 7442,2122 is 2
Step 1: Since 7442 > 2122, we apply the division lemma to 7442 and 2122, to get
7442 = 2122 x 3 + 1076
Step 2: Since the reminder 2122 ≠ 0, we apply division lemma to 1076 and 2122, to get
2122 = 1076 x 1 + 1046
Step 3: We consider the new divisor 1076 and the new remainder 1046, and apply the division lemma to get
1076 = 1046 x 1 + 30
We consider the new divisor 1046 and the new remainder 30,and apply the division lemma to get
1046 = 30 x 34 + 26
We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get
30 = 26 x 1 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7442 and 2122 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(1046,30) = HCF(1076,1046) = HCF(2122,1076) = HCF(7442,2122) .
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Frequently Asked Questions on HCF of 7442, 2122 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 7442, 2122?
Answer: HCF of 7442, 2122 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7442, 2122 using Euclid's Algorithm?
Answer: For arbitrary numbers 7442, 2122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.