Highest Common Factor of 664, 560, 822, 881 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 664, 560, 822, 881 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 560, 822, 881 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 664, 560, 822, 881 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 664, 560, 822, 881 is 1.
HCF(664, 560, 822, 881) = 1
HCF of 664, 560, 822, 881 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 560, 822, 881 is 1.
Highest Common Factor of 664,560,822,881 is 1
Step 1: Since 664 > 560, we apply the division lemma to 664 and 560, to get
664 = 560 x 1 + 104
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 104 and 560, to get
560 = 104 x 5 + 40
Step 3: We consider the new divisor 104 and the new remainder 40, and apply the division lemma to get
104 = 40 x 2 + 24
We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get
40 = 24 x 1 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 664 and 560 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(104,40) = HCF(560,104) = HCF(664,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 8, we apply the division lemma to 822 and 8, to get
822 = 8 x 102 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 822 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(822,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 881 > 2, we apply the division lemma to 881 and 2, to get
881 = 2 x 440 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 881 is 1
Notice that 1 = HCF(2,1) = HCF(881,2) .
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Frequently Asked Questions on HCF of 664, 560, 822, 881 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 664, 560, 822, 881?
Answer: HCF of 664, 560, 822, 881 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 560, 822, 881 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 560, 822, 881 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.