Highest Common Factor of 210, 350, 472, 40 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 210, 350, 472, 40 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 350, 472, 40 is 2 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 210, 350, 472, 40 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 210, 350, 472, 40 is 2.
HCF(210, 350, 472, 40) = 2
HCF of 210, 350, 472, 40 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 350, 472, 40 is 2.
Highest Common Factor of 210,350,472,40 is 2
Step 1: Since 350 > 210, we apply the division lemma to 350 and 210, to get
350 = 210 x 1 + 140
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 140 and 210, to get
210 = 140 x 1 + 70
Step 3: We consider the new divisor 140 and the new remainder 70, and apply the division lemma to get
140 = 70 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 210 and 350 is 70
Notice that 70 = HCF(140,70) = HCF(210,140) = HCF(350,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 70, we apply the division lemma to 472 and 70, to get
472 = 70 x 6 + 52
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 52 and 70, to get
70 = 52 x 1 + 18
Step 3: We consider the new divisor 52 and the new remainder 18, and apply the division lemma to get
52 = 18 x 2 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 70 and 472 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(52,18) = HCF(70,52) = HCF(472,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 2, we apply the division lemma to 40 and 2, to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 40 is 2
Notice that 2 = HCF(40,2) .
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Frequently Asked Questions on HCF of 210, 350, 472, 40 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 210, 350, 472, 40?
Answer: HCF of 210, 350, 472, 40 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 350, 472, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 350, 472, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.