Highest Common Factor of 196, 840, 360 using Euclid's algorithm
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 196, 840, 360 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 196, 840, 360 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 196, 840, 360 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 196, 840, 360 is 4.
HCF(196, 840, 360) = 4
HCF of 196, 840, 360 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 196, 840, 360 is 4.
Highest Common Factor of 196,840,360 is 4
Step 1: Since 840 > 196, we apply the division lemma to 840 and 196, to get
840 = 196 x 4 + 56
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 56 and 196, to get
196 = 56 x 3 + 28
Step 3: We consider the new divisor 56 and the new remainder 28, and apply the division lemma to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 196 and 840 is 28
Notice that 28 = HCF(56,28) = HCF(196,56) = HCF(840,196) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 360 > 28, we apply the division lemma to 360 and 28, to get
360 = 28 x 12 + 24
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 24 and 28, to get
28 = 24 x 1 + 4
Step 3: We consider the new divisor 24 and the new remainder 4, and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 28 and 360 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(360,28) .
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Frequently Asked Questions on HCF of 196, 840, 360 using Euclid's Algorithm
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 196, 840, 360?
Answer: HCF of 196, 840, 360 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 196, 840, 360 using Euclid's Algorithm?
Answer: For arbitrary numbers 196, 840, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.