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 380, 840, 292 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 380, 840, 292 is 4 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 380, 840, 292 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 380, 840, 292 is 4.
HCF(380, 840, 292) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 380, 840, 292 is 4.
Step 1: Since 840 > 380, we apply the division lemma to 840 and 380, to get
840 = 380 x 2 + 80
Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 80 and 380, to get
380 = 80 x 4 + 60
Step 3: We consider the new divisor 80 and the new remainder 60, and apply the division lemma to get
80 = 60 x 1 + 20
We consider the new divisor 60 and the new remainder 20, and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 380 and 840 is 20
Notice that 20 = HCF(60,20) = HCF(80,60) = HCF(380,80) = HCF(840,380) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 292 > 20, we apply the division lemma to 292 and 20, to get
292 = 20 x 14 + 12
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 12 and 20, to get
20 = 12 x 1 + 8
Step 3: We consider the new divisor 12 and the new remainder 8, and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 292 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(292,20) .
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 380, 840, 292?
Answer: HCF of 380, 840, 292 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 380, 840, 292 using Euclid's Algorithm?
Answer: For arbitrary numbers 380, 840, 292 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.