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 682, 291, 409, 70 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 291, 409, 70 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 682, 291, 409, 70 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 682, 291, 409, 70 is 1.
HCF(682, 291, 409, 70) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 291, 409, 70 is 1.
Step 1: Since 682 > 291, we apply the division lemma to 682 and 291, to get
682 = 291 x 2 + 100
Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 100 and 291, to get
291 = 100 x 2 + 91
Step 3: We consider the new divisor 100 and the new remainder 91, and apply the division lemma to get
100 = 91 x 1 + 9
We consider the new divisor 91 and the new remainder 9,and apply the division lemma to get
91 = 9 x 10 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 682 and 291 is 1
Notice that 1 = HCF(9,1) = HCF(91,9) = HCF(100,91) = HCF(291,100) = HCF(682,291) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 409 > 1, we apply the division lemma to 409 and 1, to get
409 = 1 x 409 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 409 is 1
Notice that 1 = HCF(409,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 1, we apply the division lemma to 70 and 1, to get
70 = 1 x 70 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 70 is 1
Notice that 1 = HCF(70,1) .
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 682, 291, 409, 70?
Answer: HCF of 682, 291, 409, 70 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 291, 409, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 291, 409, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.