Highest Common Factor of 840, 732, 608 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 840, 732, 608 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 732, 608 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 840, 732, 608 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 840, 732, 608 is 4.
HCF(840, 732, 608) = 4
HCF of 840, 732, 608 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 732, 608 is 4.
Highest Common Factor of 840,732,608 is 4
Step 1: Since 840 > 732, we apply the division lemma to 840 and 732, to get
840 = 732 x 1 + 108
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 108 and 732, to get
732 = 108 x 6 + 84
Step 3: We consider the new divisor 108 and the new remainder 84, and apply the division lemma to get
108 = 84 x 1 + 24
We consider the new divisor 84 and the new remainder 24,and apply the division lemma to get
84 = 24 x 3 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 840 and 732 is 12
Notice that 12 = HCF(24,12) = HCF(84,24) = HCF(108,84) = HCF(732,108) = HCF(840,732) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 608 > 12, we apply the division lemma to 608 and 12, to get
608 = 12 x 50 + 8
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get
12 = 8 x 1 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma 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 12 and 608 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(608,12) .
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Frequently Asked Questions on HCF of 840, 732, 608 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 840, 732, 608?
Answer: HCF of 840, 732, 608 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 732, 608 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 732, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.