Highest Common Factor of 916, 722, 776 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 916, 722, 776 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 916, 722, 776 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 916, 722, 776 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 916, 722, 776 is 2.
HCF(916, 722, 776) = 2
HCF of 916, 722, 776 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 916, 722, 776 is 2.
Highest Common Factor of 916,722,776 is 2
Step 1: Since 916 > 722, we apply the division lemma to 916 and 722, to get
916 = 722 x 1 + 194
Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 194 and 722, to get
722 = 194 x 3 + 140
Step 3: We consider the new divisor 194 and the new remainder 140, and apply the division lemma to get
194 = 140 x 1 + 54
We consider the new divisor 140 and the new remainder 54,and apply the division lemma to get
140 = 54 x 2 + 32
We consider the new divisor 54 and the new remainder 32,and apply the division lemma to get
54 = 32 x 1 + 22
We consider the new divisor 32 and the new remainder 22,and apply the division lemma to get
32 = 22 x 1 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 916 and 722 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(54,32) = HCF(140,54) = HCF(194,140) = HCF(722,194) = HCF(916,722) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 776 > 2, we apply the division lemma to 776 and 2, to get
776 = 2 x 388 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 776 is 2
Notice that 2 = HCF(776,2) .
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Frequently Asked Questions on HCF of 916, 722, 776 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 916, 722, 776?
Answer: HCF of 916, 722, 776 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 916, 722, 776 using Euclid's Algorithm?
Answer: For arbitrary numbers 916, 722, 776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.