Highest Common Factor of 399, 774, 684, 234 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 399, 774, 684, 234 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 399, 774, 684, 234 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 399, 774, 684, 234 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 399, 774, 684, 234 is 3.
HCF(399, 774, 684, 234) = 3
HCF of 399, 774, 684, 234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 399, 774, 684, 234 is 3.
Highest Common Factor of 399,774,684,234 is 3
Step 1: Since 774 > 399, we apply the division lemma to 774 and 399, to get
774 = 399 x 1 + 375
Step 2: Since the reminder 399 ≠ 0, we apply division lemma to 375 and 399, to get
399 = 375 x 1 + 24
Step 3: We consider the new divisor 375 and the new remainder 24, and apply the division lemma to get
375 = 24 x 15 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 399 and 774 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(375,24) = HCF(399,375) = HCF(774,399) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 3, we apply the division lemma to 684 and 3, to get
684 = 3 x 228 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 684 is 3
Notice that 3 = HCF(684,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 234 > 3, we apply the division lemma to 234 and 3, to get
234 = 3 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 234 is 3
Notice that 3 = HCF(234,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 399, 774, 684, 234 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 399, 774, 684, 234?
Answer: HCF of 399, 774, 684, 234 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 399, 774, 684, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 399, 774, 684, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.