Highest Common Factor of 1052, 676 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 1052, 676 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 1052, 676 is 4 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 1052, 676 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 1052, 676 is 4.
HCF(1052, 676) = 4
HCF of 1052, 676 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1052, 676 is 4.
Highest Common Factor of 1052,676 is 4
Step 1: Since 1052 > 676, we apply the division lemma to 1052 and 676, to get
1052 = 676 x 1 + 376
Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 376 and 676, to get
676 = 376 x 1 + 300
Step 3: We consider the new divisor 376 and the new remainder 300, and apply the division lemma to get
376 = 300 x 1 + 76
We consider the new divisor 300 and the new remainder 76,and apply the division lemma to get
300 = 76 x 3 + 72
We consider the new divisor 76 and the new remainder 72,and apply the division lemma to get
76 = 72 x 1 + 4
We consider the new divisor 72 and the new remainder 4,and apply the division lemma to get
72 = 4 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 1052 and 676 is 4
Notice that 4 = HCF(72,4) = HCF(76,72) = HCF(300,76) = HCF(376,300) = HCF(676,376) = HCF(1052,676) .
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Frequently Asked Questions on HCF of 1052, 676 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 1052, 676?
Answer: HCF of 1052, 676 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1052, 676 using Euclid's Algorithm?
Answer: For arbitrary numbers 1052, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.