Highest Common Factor of 100, 640, 310, 70 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 100, 640, 310, 70 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 100, 640, 310, 70 is 10 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 100, 640, 310, 70 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 100, 640, 310, 70 is 10.
HCF(100, 640, 310, 70) = 10
HCF of 100, 640, 310, 70 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 100, 640, 310, 70 is 10.
Highest Common Factor of 100,640,310,70 is 10
Step 1: Since 640 > 100, we apply the division lemma to 640 and 100, to get
640 = 100 x 6 + 40
Step 2: Since the reminder 100 ≠ 0, we apply division lemma to 40 and 100, to get
100 = 40 x 2 + 20
Step 3: We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 100 and 640 is 20
Notice that 20 = HCF(40,20) = HCF(100,40) = HCF(640,100) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 310 > 20, we apply the division lemma to 310 and 20, to get
310 = 20 x 15 + 10
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 20 and 310 is 10
Notice that 10 = HCF(20,10) = HCF(310,20) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 10, we apply the division lemma to 70 and 10, to get
70 = 10 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 70 is 10
Notice that 10 = HCF(70,10) .
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Frequently Asked Questions on HCF of 100, 640, 310, 70 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 100, 640, 310, 70?
Answer: HCF of 100, 640, 310, 70 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 100, 640, 310, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 100, 640, 310, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.