Highest Common Factor of 669, 972, 690 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 669, 972, 690 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 972, 690 is 3 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 669, 972, 690 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 669, 972, 690 is 3.
HCF(669, 972, 690) = 3
HCF of 669, 972, 690 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 972, 690 is 3.
Highest Common Factor of 669,972,690 is 3
Step 1: Since 972 > 669, we apply the division lemma to 972 and 669, to get
972 = 669 x 1 + 303
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 303 and 669, to get
669 = 303 x 2 + 63
Step 3: We consider the new divisor 303 and the new remainder 63, and apply the division lemma to get
303 = 63 x 4 + 51
We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get
63 = 51 x 1 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 972 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(303,63) = HCF(669,303) = HCF(972,669) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 690 > 3, we apply the division lemma to 690 and 3, to get
690 = 3 x 230 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 690 is 3
Notice that 3 = HCF(690,3) .
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Frequently Asked Questions on HCF of 669, 972, 690 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 669, 972, 690?
Answer: HCF of 669, 972, 690 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 972, 690 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 972, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.