Highest Common Factor of 222, 986, 860, 16 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 222, 986, 860, 16 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 986, 860, 16 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 222, 986, 860, 16 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 222, 986, 860, 16 is 2.
HCF(222, 986, 860, 16) = 2
HCF of 222, 986, 860, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 222, 986, 860, 16 is 2.
Highest Common Factor of 222,986,860,16 is 2
Step 1: Since 986 > 222, we apply the division lemma to 986 and 222, to get
986 = 222 x 4 + 98
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 98 and 222, to get
222 = 98 x 2 + 26
Step 3: We consider the new divisor 98 and the new remainder 26, and apply the division lemma to get
98 = 26 x 3 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 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 222 and 986 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(222,98) = HCF(986,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 2, we apply the division lemma to 860 and 2, to get
860 = 2 x 430 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 860 is 2
Notice that 2 = HCF(860,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2
Notice that 2 = HCF(16,2) .
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Frequently Asked Questions on HCF of 222, 986, 860, 16 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 222, 986, 860, 16?
Answer: HCF of 222, 986, 860, 16 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 986, 860, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 986, 860, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.