Highest Common Factor of 840, 291, 560 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 840, 291, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 291, 560 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 840, 291, 560 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 840, 291, 560 is 1.
HCF(840, 291, 560) = 1
HCF of 840, 291, 560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 291, 560 is 1.
Highest Common Factor of 840,291,560 is 1
Step 1: Since 840 > 291, we apply the division lemma to 840 and 291, to get
840 = 291 x 2 + 258
Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 258 and 291, to get
291 = 258 x 1 + 33
Step 3: We consider the new divisor 258 and the new remainder 33, and apply the division lemma to get
258 = 33 x 7 + 27
We consider the new divisor 33 and the new remainder 27,and apply the division lemma to get
33 = 27 x 1 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 840 and 291 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(258,33) = HCF(291,258) = HCF(840,291) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 3, we apply the division lemma to 560 and 3, to get
560 = 3 x 186 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 560 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(560,3) .
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Frequently Asked Questions on HCF of 840, 291, 560 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 840, 291, 560?
Answer: HCF of 840, 291, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 291, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 291, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.