Highest Common Factor of 972, 9922 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 972, 9922 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 9922 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 972, 9922 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 972, 9922 is 2.
HCF(972, 9922) = 2
HCF of 972, 9922 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 9922 is 2.
Highest Common Factor of 972,9922 is 2
Step 1: Since 9922 > 972, we apply the division lemma to 9922 and 972, to get
9922 = 972 x 10 + 202
Step 2: Since the reminder 972 ≠ 0, we apply division lemma to 202 and 972, to get
972 = 202 x 4 + 164
Step 3: We consider the new divisor 202 and the new remainder 164, and apply the division lemma to get
202 = 164 x 1 + 38
We consider the new divisor 164 and the new remainder 38,and apply the division lemma to get
164 = 38 x 4 + 12
We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get
38 = 12 x 3 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 972 and 9922 is 2
Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(164,38) = HCF(202,164) = HCF(972,202) = HCF(9922,972) .
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Frequently Asked Questions on HCF of 972, 9922 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 972, 9922?
Answer: HCF of 972, 9922 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 9922 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 9922 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.