Highest Common Factor of 490, 678, 828 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 490, 678, 828 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 678, 828 is 2 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 490, 678, 828 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 490, 678, 828 is 2.
HCF(490, 678, 828) = 2
HCF of 490, 678, 828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 490, 678, 828 is 2.
Highest Common Factor of 490,678,828 is 2
Step 1: Since 678 > 490, we apply the division lemma to 678 and 490, to get
678 = 490 x 1 + 188
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 188 and 490, to get
490 = 188 x 2 + 114
Step 3: We consider the new divisor 188 and the new remainder 114, and apply the division lemma to get
188 = 114 x 1 + 74
We consider the new divisor 114 and the new remainder 74,and apply the division lemma to get
114 = 74 x 1 + 40
We consider the new divisor 74 and the new remainder 40,and apply the division lemma to get
74 = 40 x 1 + 34
We consider the new divisor 40 and the new remainder 34,and apply the division lemma to get
40 = 34 x 1 + 6
We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get
34 = 6 x 5 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 490 and 678 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(40,34) = HCF(74,40) = HCF(114,74) = HCF(188,114) = HCF(490,188) = HCF(678,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 828 > 2, we apply the division lemma to 828 and 2, to get
828 = 2 x 414 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 828 is 2
Notice that 2 = HCF(828,2) .
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Frequently Asked Questions on HCF of 490, 678, 828 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 490, 678, 828?
Answer: HCF of 490, 678, 828 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 678, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 678, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.