Highest Common Factor of 969, 600, 964 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 969, 600, 964 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 969, 600, 964 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 969, 600, 964 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 969, 600, 964 is 1.
HCF(969, 600, 964) = 1
HCF of 969, 600, 964 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 969, 600, 964 is 1.
Highest Common Factor of 969,600,964 is 1
Step 1: Since 969 > 600, we apply the division lemma to 969 and 600, to get
969 = 600 x 1 + 369
Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 369 and 600, to get
600 = 369 x 1 + 231
Step 3: We consider the new divisor 369 and the new remainder 231, and apply the division lemma to get
369 = 231 x 1 + 138
We consider the new divisor 231 and the new remainder 138,and apply the division lemma to get
231 = 138 x 1 + 93
We consider the new divisor 138 and the new remainder 93,and apply the division lemma to get
138 = 93 x 1 + 45
We consider the new divisor 93 and the new remainder 45,and apply the division lemma to get
93 = 45 x 2 + 3
We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 969 and 600 is 3
Notice that 3 = HCF(45,3) = HCF(93,45) = HCF(138,93) = HCF(231,138) = HCF(369,231) = HCF(600,369) = HCF(969,600) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 964 > 3, we apply the division lemma to 964 and 3, to get
964 = 3 x 321 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 964 is 1
Notice that 1 = HCF(3,1) = HCF(964,3) .
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Frequently Asked Questions on HCF of 969, 600, 964 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 969, 600, 964?
Answer: HCF of 969, 600, 964 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 969, 600, 964 using Euclid's Algorithm?
Answer: For arbitrary numbers 969, 600, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.