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 364, 210, 784 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 210, 784 is 14 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 364, 210, 784 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 364, 210, 784 is 14.
HCF(364, 210, 784) = 14
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 210, 784 is 14.
Step 1: Since 364 > 210, we apply the division lemma to 364 and 210, to get
364 = 210 x 1 + 154
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 154 and 210, to get
210 = 154 x 1 + 56
Step 3: We consider the new divisor 154 and the new remainder 56, and apply the division lemma to get
154 = 56 x 2 + 42
We consider the new divisor 56 and the new remainder 42,and apply the division lemma to get
56 = 42 x 1 + 14
We consider the new divisor 42 and the new remainder 14,and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 364 and 210 is 14
Notice that 14 = HCF(42,14) = HCF(56,42) = HCF(154,56) = HCF(210,154) = HCF(364,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 784 > 14, we apply the division lemma to 784 and 14, to get
784 = 14 x 56 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 784 is 14
Notice that 14 = HCF(784,14) .
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 364, 210, 784?
Answer: HCF of 364, 210, 784 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 210, 784 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 210, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.