Highest Common Factor of 876, 360, 116, 272 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 876, 360, 116, 272 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 876, 360, 116, 272 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 876, 360, 116, 272 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 876, 360, 116, 272 is 4.
HCF(876, 360, 116, 272) = 4
HCF of 876, 360, 116, 272 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 876, 360, 116, 272 is 4.
Highest Common Factor of 876,360,116,272 is 4
Step 1: Since 876 > 360, we apply the division lemma to 876 and 360, to get
876 = 360 x 2 + 156
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 156 and 360, to get
360 = 156 x 2 + 48
Step 3: We consider the new divisor 156 and the new remainder 48, and apply the division lemma to get
156 = 48 x 3 + 12
We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 876 and 360 is 12
Notice that 12 = HCF(48,12) = HCF(156,48) = HCF(360,156) = HCF(876,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 12, we apply the division lemma to 116 and 12, to get
116 = 12 x 9 + 8
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get
12 = 8 x 1 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 116 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(116,12) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 272 > 4, we apply the division lemma to 272 and 4, to get
272 = 4 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 272 is 4
Notice that 4 = HCF(272,4) .
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Frequently Asked Questions on HCF of 876, 360, 116, 272 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 876, 360, 116, 272?
Answer: HCF of 876, 360, 116, 272 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 876, 360, 116, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 876, 360, 116, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
