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 238, 840, 435 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 840, 435 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 238, 840, 435 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 238, 840, 435 is 1.
HCF(238, 840, 435) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 238, 840, 435 is 1.
Step 1: Since 840 > 238, we apply the division lemma to 840 and 238, to get
840 = 238 x 3 + 126
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 126 and 238, to get
238 = 126 x 1 + 112
Step 3: We consider the new divisor 126 and the new remainder 112, and apply the division lemma to get
126 = 112 x 1 + 14
We consider the new divisor 112 and the new remainder 14, and apply the division lemma to get
112 = 14 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 238 and 840 is 14
Notice that 14 = HCF(112,14) = HCF(126,112) = HCF(238,126) = HCF(840,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 435 > 14, we apply the division lemma to 435 and 14, to get
435 = 14 x 31 + 1
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 1 and 14, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 435 is 1
Notice that 1 = HCF(14,1) = HCF(435,14) .
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 238, 840, 435?
Answer: HCF of 238, 840, 435 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 840, 435 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 840, 435 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.