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 610, 372, 404 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 372, 404 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 610, 372, 404 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 610, 372, 404 is 2.
HCF(610, 372, 404) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 610, 372, 404 is 2.
Step 1: Since 610 > 372, we apply the division lemma to 610 and 372, to get
610 = 372 x 1 + 238
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 238 and 372, to get
372 = 238 x 1 + 134
Step 3: We consider the new divisor 238 and the new remainder 134, and apply the division lemma to get
238 = 134 x 1 + 104
We consider the new divisor 134 and the new remainder 104,and apply the division lemma to get
134 = 104 x 1 + 30
We consider the new divisor 104 and the new remainder 30,and apply the division lemma to get
104 = 30 x 3 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 610 and 372 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(104,30) = HCF(134,104) = HCF(238,134) = HCF(372,238) = HCF(610,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 404 > 2, we apply the division lemma to 404 and 2, to get
404 = 2 x 202 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 404 is 2
Notice that 2 = HCF(404,2) .
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 610, 372, 404?
Answer: HCF of 610, 372, 404 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 372, 404 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 372, 404 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.