Highest Common Factor of 66, 22, 14, 322 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 66, 22, 14, 322 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 66, 22, 14, 322 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 66, 22, 14, 322 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 66, 22, 14, 322 is 2.
HCF(66, 22, 14, 322) = 2
HCF of 66, 22, 14, 322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 66, 22, 14, 322 is 2.
Highest Common Factor of 66,22,14,322 is 2
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 66 and 22 is 22
Notice that 22 = HCF(66,22) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 14, we apply the division lemma to 22 and 14, to get
22 = 14 x 1 + 8
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 8 and 14, to get
14 = 8 x 1 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 14 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 322 > 2, we apply the division lemma to 322 and 2, to get
322 = 2 x 161 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 322 is 2
Notice that 2 = HCF(322,2) .
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Frequently Asked Questions on HCF of 66, 22, 14, 322 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 66, 22, 14, 322?
Answer: HCF of 66, 22, 14, 322 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 66, 22, 14, 322 using Euclid's Algorithm?
Answer: For arbitrary numbers 66, 22, 14, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.