Highest Common Factor of 984, 22218 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 984, 22218 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 22218 is 6 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 984, 22218 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 984, 22218 is 6.
HCF(984, 22218) = 6
HCF of 984, 22218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 22218 is 6.
Highest Common Factor of 984,22218 is 6
Step 1: Since 22218 > 984, we apply the division lemma to 22218 and 984, to get
22218 = 984 x 22 + 570
Step 2: Since the reminder 984 ≠ 0, we apply division lemma to 570 and 984, to get
984 = 570 x 1 + 414
Step 3: We consider the new divisor 570 and the new remainder 414, and apply the division lemma to get
570 = 414 x 1 + 156
We consider the new divisor 414 and the new remainder 156,and apply the division lemma to get
414 = 156 x 2 + 102
We consider the new divisor 156 and the new remainder 102,and apply the division lemma to get
156 = 102 x 1 + 54
We consider the new divisor 102 and the new remainder 54,and apply the division lemma to get
102 = 54 x 1 + 48
We consider the new divisor 54 and the new remainder 48,and apply the division lemma to get
54 = 48 x 1 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 984 and 22218 is 6
Notice that 6 = HCF(48,6) = HCF(54,48) = HCF(102,54) = HCF(156,102) = HCF(414,156) = HCF(570,414) = HCF(984,570) = HCF(22218,984) .
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Frequently Asked Questions on HCF of 984, 22218 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 984, 22218?
Answer: HCF of 984, 22218 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 22218 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 22218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.