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 676, 497, 268, 43 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 497, 268, 43 is 1 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 676, 497, 268, 43 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 676, 497, 268, 43 is 1.
HCF(676, 497, 268, 43) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 676, 497, 268, 43 is 1.
Step 1: Since 676 > 497, we apply the division lemma to 676 and 497, to get
676 = 497 x 1 + 179
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 179 and 497, to get
497 = 179 x 2 + 139
Step 3: We consider the new divisor 179 and the new remainder 139, and apply the division lemma to get
179 = 139 x 1 + 40
We consider the new divisor 139 and the new remainder 40,and apply the division lemma to get
139 = 40 x 3 + 19
We consider the new divisor 40 and the new remainder 19,and apply the division lemma to get
40 = 19 x 2 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 676 and 497 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(40,19) = HCF(139,40) = HCF(179,139) = HCF(497,179) = HCF(676,497) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 268 > 1, we apply the division lemma to 268 and 1, to get
268 = 1 x 268 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 268 is 1
Notice that 1 = HCF(268,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43 > 1, we apply the division lemma to 43 and 1, to get
43 = 1 x 43 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 43 is 1
Notice that 1 = HCF(43,1) .
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 676, 497, 268, 43?
Answer: HCF of 676, 497, 268, 43 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 497, 268, 43 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 497, 268, 43 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.