Highest Common Factor of 861, 552 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 861, 552 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 552 is 3 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 861, 552 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 861, 552 is 3.
HCF(861, 552) = 3
HCF of 861, 552 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 861, 552 is 3.
Highest Common Factor of 861,552 is 3
Step 1: Since 861 > 552, we apply the division lemma to 861 and 552, to get
861 = 552 x 1 + 309
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 309 and 552, to get
552 = 309 x 1 + 243
Step 3: We consider the new divisor 309 and the new remainder 243, and apply the division lemma to get
309 = 243 x 1 + 66
We consider the new divisor 243 and the new remainder 66,and apply the division lemma to get
243 = 66 x 3 + 45
We consider the new divisor 66 and the new remainder 45,and apply the division lemma to get
66 = 45 x 1 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 861 and 552 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(66,45) = HCF(243,66) = HCF(309,243) = HCF(552,309) = HCF(861,552) .
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Frequently Asked Questions on HCF of 861, 552 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 861, 552?
Answer: HCF of 861, 552 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 552 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 552 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
