Highest Common Factor of 924, 532, 661 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 924, 532, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 924, 532, 661 is 1 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 924, 532, 661 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 924, 532, 661 is 1.
HCF(924, 532, 661) = 1
HCF of 924, 532, 661 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 924, 532, 661 is 1.
Highest Common Factor of 924,532,661 is 1
Step 1: Since 924 > 532, we apply the division lemma to 924 and 532, to get
924 = 532 x 1 + 392
Step 2: Since the reminder 532 ≠ 0, we apply division lemma to 392 and 532, to get
532 = 392 x 1 + 140
Step 3: We consider the new divisor 392 and the new remainder 140, and apply the division lemma to get
392 = 140 x 2 + 112
We consider the new divisor 140 and the new remainder 112,and apply the division lemma to get
140 = 112 x 1 + 28
We consider the new divisor 112 and the new remainder 28,and apply the division lemma to get
112 = 28 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 924 and 532 is 28
Notice that 28 = HCF(112,28) = HCF(140,112) = HCF(392,140) = HCF(532,392) = HCF(924,532) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 661 > 28, we apply the division lemma to 661 and 28, to get
661 = 28 x 23 + 17
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 17 and 28, to get
28 = 17 x 1 + 11
Step 3: We consider the new divisor 17 and the new remainder 11, and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 28 and 661 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(661,28) .
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Frequently Asked Questions on HCF of 924, 532, 661 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 924, 532, 661?
Answer: HCF of 924, 532, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 924, 532, 661 using Euclid's Algorithm?
Answer: For arbitrary numbers 924, 532, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.