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 420, 693, 337 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 693, 337 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 420, 693, 337 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 420, 693, 337 is 1.
HCF(420, 693, 337) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 693, 337 is 1.
Step 1: Since 693 > 420, we apply the division lemma to 693 and 420, to get
693 = 420 x 1 + 273
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 273 and 420, to get
420 = 273 x 1 + 147
Step 3: We consider the new divisor 273 and the new remainder 147, and apply the division lemma to get
273 = 147 x 1 + 126
We consider the new divisor 147 and the new remainder 126,and apply the division lemma to get
147 = 126 x 1 + 21
We consider the new divisor 126 and the new remainder 21,and apply the division lemma to get
126 = 21 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 420 and 693 is 21
Notice that 21 = HCF(126,21) = HCF(147,126) = HCF(273,147) = HCF(420,273) = HCF(693,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 337 > 21, we apply the division lemma to 337 and 21, to get
337 = 21 x 16 + 1
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 1 and 21, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 337 is 1
Notice that 1 = HCF(21,1) = HCF(337,21) .
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 420, 693, 337?
Answer: HCF of 420, 693, 337 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 693, 337 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 693, 337 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.