Highest Common Factor of 976, 824, 106 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 976, 824, 106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 976, 824, 106 is 2 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 976, 824, 106 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 976, 824, 106 is 2.
HCF(976, 824, 106) = 2
HCF of 976, 824, 106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 976, 824, 106 is 2.
Highest Common Factor of 976,824,106 is 2
Step 1: Since 976 > 824, we apply the division lemma to 976 and 824, to get
976 = 824 x 1 + 152
Step 2: Since the reminder 824 ≠ 0, we apply division lemma to 152 and 824, to get
824 = 152 x 5 + 64
Step 3: We consider the new divisor 152 and the new remainder 64, and apply the division lemma to get
152 = 64 x 2 + 24
We consider the new divisor 64 and the new remainder 24,and apply the division lemma to get
64 = 24 x 2 + 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 976 and 824 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(152,64) = HCF(824,152) = HCF(976,824) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 8, we apply the division lemma to 106 and 8, to get
106 = 8 x 13 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 106 is 2
Notice that 2 = HCF(8,2) = HCF(106,8) .
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Frequently Asked Questions on HCF of 976, 824, 106 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 976, 824, 106?
Answer: HCF of 976, 824, 106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 976, 824, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 976, 824, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.