Highest Common Factor of 880, 506, 66 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 880, 506, 66 i.e. 22 the largest integer that leaves a remainder zero for all numbers.
HCF of 880, 506, 66 is 22 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 880, 506, 66 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 880, 506, 66 is 22.
HCF(880, 506, 66) = 22
HCF of 880, 506, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 880, 506, 66 is 22.
Highest Common Factor of 880,506,66 is 22
Step 1: Since 880 > 506, we apply the division lemma to 880 and 506, to get
880 = 506 x 1 + 374
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 374 and 506, to get
506 = 374 x 1 + 132
Step 3: We consider the new divisor 374 and the new remainder 132, and apply the division lemma to get
374 = 132 x 2 + 110
We consider the new divisor 132 and the new remainder 110,and apply the division lemma to get
132 = 110 x 1 + 22
We consider the new divisor 110 and the new remainder 22,and apply the division lemma to get
110 = 22 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 880 and 506 is 22
Notice that 22 = HCF(110,22) = HCF(132,110) = HCF(374,132) = HCF(506,374) = HCF(880,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 22, we apply the division lemma to 66 and 22, to get
66 = 22 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 22 and 66 is 22
Notice that 22 = HCF(66,22) .
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Frequently Asked Questions on HCF of 880, 506, 66 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 880, 506, 66?
Answer: HCF of 880, 506, 66 is 22 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 880, 506, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 880, 506, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.