Highest Common Factor of 876, 552, 612 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 876, 552, 612 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 876, 552, 612 is 12 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 876, 552, 612 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 876, 552, 612 is 12.
HCF(876, 552, 612) = 12
HCF of 876, 552, 612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 876, 552, 612 is 12.
Highest Common Factor of 876,552,612 is 12
Step 1: Since 876 > 552, we apply the division lemma to 876 and 552, to get
876 = 552 x 1 + 324
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 324 and 552, to get
552 = 324 x 1 + 228
Step 3: We consider the new divisor 324 and the new remainder 228, and apply the division lemma to get
324 = 228 x 1 + 96
We consider the new divisor 228 and the new remainder 96,and apply the division lemma to get
228 = 96 x 2 + 36
We consider the new divisor 96 and the new remainder 36,and apply the division lemma to get
96 = 36 x 2 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 876 and 552 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(96,36) = HCF(228,96) = HCF(324,228) = HCF(552,324) = HCF(876,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 12, we apply the division lemma to 612 and 12, to get
612 = 12 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 612 is 12
Notice that 12 = HCF(612,12) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 876, 552, 612 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 876, 552, 612?
Answer: HCF of 876, 552, 612 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 876, 552, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 876, 552, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.