Highest Common Factor of 412, 672, 976 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 412, 672, 976 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 672, 976 is 4 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 412, 672, 976 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 412, 672, 976 is 4.
HCF(412, 672, 976) = 4
HCF of 412, 672, 976 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 672, 976 is 4.
Highest Common Factor of 412,672,976 is 4
Step 1: Since 672 > 412, we apply the division lemma to 672 and 412, to get
672 = 412 x 1 + 260
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 260 and 412, to get
412 = 260 x 1 + 152
Step 3: We consider the new divisor 260 and the new remainder 152, and apply the division lemma to get
260 = 152 x 1 + 108
We consider the new divisor 152 and the new remainder 108,and apply the division lemma to get
152 = 108 x 1 + 44
We consider the new divisor 108 and the new remainder 44,and apply the division lemma to get
108 = 44 x 2 + 20
We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 672 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(108,44) = HCF(152,108) = HCF(260,152) = HCF(412,260) = HCF(672,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 976 > 4, we apply the division lemma to 976 and 4, to get
976 = 4 x 244 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 976 is 4
Notice that 4 = HCF(976,4) .
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Frequently Asked Questions on HCF of 412, 672, 976 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 412, 672, 976?
Answer: HCF of 412, 672, 976 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 672, 976 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 672, 976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
