Highest Common Factor of 624, 960, 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 624, 960, 964 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 624, 960, 964 is 4 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 624, 960, 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 624, 960, 964 is 4.
HCF(624, 960, 964) = 4
HCF of 624, 960, 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 624, 960, 964 is 4.
Highest Common Factor of 624,960,964 is 4
Step 1: Since 960 > 624, we apply the division lemma to 960 and 624, to get
960 = 624 x 1 + 336
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 336 and 624, to get
624 = 336 x 1 + 288
Step 3: We consider the new divisor 336 and the new remainder 288, and apply the division lemma to get
336 = 288 x 1 + 48
We consider the new divisor 288 and the new remainder 48, and apply the division lemma to get
288 = 48 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 624 and 960 is 48
Notice that 48 = HCF(288,48) = HCF(336,288) = HCF(624,336) = HCF(960,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 964 > 48, we apply the division lemma to 964 and 48, to get
964 = 48 x 20 + 4
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 4 and 48, to get
48 = 4 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 48 and 964 is 4
Notice that 4 = HCF(48,4) = HCF(964,48) .
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Frequently Asked Questions on HCF of 624, 960, 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 624, 960, 964?
Answer: HCF of 624, 960, 964 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 624, 960, 964 using Euclid's Algorithm?
Answer: For arbitrary numbers 624, 960, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.