Highest Common Factor of 936, 7221 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 936, 7221 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 936, 7221 is 3 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 936, 7221 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 936, 7221 is 3.
HCF(936, 7221) = 3
HCF of 936, 7221 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 936, 7221 is 3.
Highest Common Factor of 936,7221 is 3
Step 1: Since 7221 > 936, we apply the division lemma to 7221 and 936, to get
7221 = 936 x 7 + 669
Step 2: Since the reminder 936 ≠ 0, we apply division lemma to 669 and 936, to get
936 = 669 x 1 + 267
Step 3: We consider the new divisor 669 and the new remainder 267, and apply the division lemma to get
669 = 267 x 2 + 135
We consider the new divisor 267 and the new remainder 135,and apply the division lemma to get
267 = 135 x 1 + 132
We consider the new divisor 135 and the new remainder 132,and apply the division lemma to get
135 = 132 x 1 + 3
We consider the new divisor 132 and the new remainder 3,and apply the division lemma to get
132 = 3 x 44 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 936 and 7221 is 3
Notice that 3 = HCF(132,3) = HCF(135,132) = HCF(267,135) = HCF(669,267) = HCF(936,669) = HCF(7221,936) .
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Frequently Asked Questions on HCF of 936, 7221 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 936, 7221?
Answer: HCF of 936, 7221 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 936, 7221 using Euclid's Algorithm?
Answer: For arbitrary numbers 936, 7221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.