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 828, 669, 228 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 669, 228 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 828, 669, 228 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 828, 669, 228 is 3.
HCF(828, 669, 228) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 669, 228 is 3.
Step 1: Since 828 > 669, we apply the division lemma to 828 and 669, to get
828 = 669 x 1 + 159
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 159 and 669, to get
669 = 159 x 4 + 33
Step 3: We consider the new divisor 159 and the new remainder 33, and apply the division lemma to get
159 = 33 x 4 + 27
We consider the new divisor 33 and the new remainder 27,and apply the division lemma to get
33 = 27 x 1 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 828 and 669 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(159,33) = HCF(669,159) = HCF(828,669) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 228 > 3, we apply the division lemma to 228 and 3, to get
228 = 3 x 76 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 228 is 3
Notice that 3 = HCF(228,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 828, 669, 228?
Answer: HCF of 828, 669, 228 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 669, 228 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 669, 228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.