Highest Common Factor of 824, 120, 712, 954 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 824, 120, 712, 954 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 120, 712, 954 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 824, 120, 712, 954 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 824, 120, 712, 954 is 2.
HCF(824, 120, 712, 954) = 2
HCF of 824, 120, 712, 954 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 120, 712, 954 is 2.
Highest Common Factor of 824,120,712,954 is 2
Step 1: Since 824 > 120, we apply the division lemma to 824 and 120, to get
824 = 120 x 6 + 104
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 104 and 120, to get
120 = 104 x 1 + 16
Step 3: We consider the new divisor 104 and the new remainder 16, and apply the division lemma to get
104 = 16 x 6 + 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 824 and 120 is 8
Notice that 8 = HCF(16,8) = HCF(104,16) = HCF(120,104) = HCF(824,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 712 > 8, we apply the division lemma to 712 and 8, to get
712 = 8 x 89 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 712 is 8
Notice that 8 = HCF(712,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 954 > 8, we apply the division lemma to 954 and 8, to get
954 = 8 x 119 + 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 954 is 2
Notice that 2 = HCF(8,2) = HCF(954,8) .
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Frequently Asked Questions on HCF of 824, 120, 712, 954 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 824, 120, 712, 954?
Answer: HCF of 824, 120, 712, 954 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 120, 712, 954 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 120, 712, 954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.