Highest Common Factor of 440, 624, 420 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 440, 624, 420 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 624, 420 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 440, 624, 420 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 440, 624, 420 is 4.
HCF(440, 624, 420) = 4
HCF of 440, 624, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 624, 420 is 4.
Highest Common Factor of 440,624,420 is 4
Step 1: Since 624 > 440, we apply the division lemma to 624 and 440, to get
624 = 440 x 1 + 184
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 184 and 440, to get
440 = 184 x 2 + 72
Step 3: We consider the new divisor 184 and the new remainder 72, and apply the division lemma to get
184 = 72 x 2 + 40
We consider the new divisor 72 and the new remainder 40,and apply the division lemma to get
72 = 40 x 1 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 440 and 624 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(72,40) = HCF(184,72) = HCF(440,184) = HCF(624,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 420 > 8, we apply the division lemma to 420 and 8, to get
420 = 8 x 52 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 420 is 4
Notice that 4 = HCF(8,4) = HCF(420,8) .
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Frequently Asked Questions on HCF of 440, 624, 420 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 440, 624, 420?
Answer: HCF of 440, 624, 420 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 624, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 624, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.